A question I have frequently used in a conversation with someone who is promoting a staunch insistance on Biblical literalism is to ask them, "When was Eve created?" The strict answer is at the end of creation in Genesis 2:21-23. If, however you with or without a friend have done the exercise I gave you you will notice some conflicts with that answer.
In chapter 1 of Genesis humanity is created male and female as the last act of creation as the capstone of creation and humanity is created simultaneously in the image of God, male and female.
In chapter 2 the story of creation begins with a presentation of a personafied God as intimately involved with the creation of Adam creating him out of the red soil and blowing divine breath into Adam. Then in chapter 2 a variety of creative acts take place and the animals (all of which in Genesis 1 were created before the creation of humanity on the fifth and sixth days) are brought to Adam to be named but none is a suitable partner for Adam and then God causes sleep to fall upon Adam and Eve is created out of a piece from Adam's own side and is identified by Adam as flesh of my flesh and bone of my bone.
Hopefully, by answering questions I gave you and by working on the chapters separately with a friend and comparing your answers to those questions you can see the differences and problems trying to approach this material literally poses and how trying to resolve it might lead to all sort of constructed answers not within the material.
Besides those differences there are more things unique to each chapter that we can see. In Genesis 1 the name used for the divine presence is simply God but in Genesis 2 beginning with the 4th verse the divine address changes Lord God. The consistency of these two names is steadfast and reliable throughout these chapters. In addition, God's power in creation in chapter1 is exercised through God speaking into existance the creative power and the resulting reality. In the story from Genesis 2:4ff the Lord God is more personally involved in the events and is a personafied presence in the midst of creating. Lastly, of the differences I will call to your attention is that Genesis 1 has the structure of seven days, each day God creates of reality and sees that the creation is good and each day comes to an end with, "And there was evening, and there was morning--" and the day is numbered. And as the sixth day closes after humanity is created God looks at it all and says it is very good.
There is richness in these two stories that is lost when we rush to merge them together and don't allow them to both stand uniquely before us.
But what does gaining an understanding of these two creation accounts gain for us when we see we can no longer hold to literalist assumptions about them being one story. The first reflex for many people seems to be, "Well, which one is true? Which of these stories is how it happened?" In that response, we reveal ourselves to be modern thinkers who approach the world differently from the Biblical authors. We want facts, not truth, facts. To us facts are the only conveyor of real truth. Anything less than facts is insufficient for my faith, my trust.
In that demand to provided the facts of creation we expose ourselves once again as those broken saints. "If I can't have facts I can't believe." "If it isn't history then it isn't true." In fear and irony the literalist clings to the only way of thinking they know as members of modernity.
In contrast to this rigid way of thinking the Bible is filled with a steady stream of new ways of seeing and thinking. God uses women and gentiles to further the story of salvation history. This was incredibly offensive to the "in group" of the chosen people. Again and again the stories of God's people find the expected changing and amazing things about them and their relationship to God renewed and different.
Sometimes these new ways of seeing the world and God's work take away the very thoughts that have held us captive to our clay pot theologies. Consider this. If the Bible includes two extended stories about the how of creation and fragments of a couple more then is how the right question? And if how is not the right question or the right truth we are to draw from these stories is there any real conflict with evolution and its attempt to answer the question how?
And if these stories are not about how then what understanding of truth might they be about and where might our journey with the text take us. If not how, maybe "who" and "what?" And the answer of the Genesis stories to those questions is a constant, "God created everything." Everything from the smallest particles of quantum physics to the vast expanse of space measured in light years and more. That everything includes God creating life, including you and me, whether best explained by the latest refinement of evolutionary theory or something better yet to come. You see science is our companion on this journey. Science only fails when it stops testing its assumptions about creation, ironically that is, also, true of faith. Faith, scriptural faith, is always open to new ways of seeing and doing God's will and living God's Word in the world every day.
One of the things about science is that it is on a constantly self correcting journey. When facts emerge that conflict with the current understanding or theory, the facts aren't rejected. Rather the theory is altered and refined in a manner that accounts for the new information.
Healing sinners with living faith move through life in the same manner. When we recognize that God is giving us a new word and a new vision for the future then we test it and study it and if it changes our world view from polytheism to monotheism, we change with that new insight. When the people of Israel and Judah were cast out into exile and discovered that their God was not captive to the borders of the Promised Land they discovered they could sing the Lord God's song in a strange land. When we discover that we are blessed with multiple stories of creation we do not need to be frozen in fear but instead move out in faith to discover how this new way of seeing strengthens us for our journey.