Contradiction: How Was Eve Created?

Contradictions in Genesis on How Eve Was Created

Genesis has contradictory accounts of when and how Eve, the first woman, was created. The Bible's first creation story says that Eve was created at the same time as Adam. The Bible's second creation story says that Adam was created first, then all the animals were created, and finally Eve was created from one of Adam's ribs. So when was Eve created relative to Adam and other animals?

First Human Creation Story

Genesis 1:27: So God created man in his own image, in the image of God created he him; male and female created he them.

Second Human Creation Story

Genesis 2:18-22: And the Lord God said, It is not good that the man should be alone; I will make him an help meet for him. And out of the ground the Lord God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof.
And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him. And the Lord God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof; And the rib, which the Lord God had taken from man, made he a woman, and brought her unto the man.

It's interesting that so many people remember the second story about Eve being created from Adam's rib, but not the first one. Granted, it's a more engaging story with more going on, but is it mere coincidence that it's also the story in which woman is portrayed as secondary to man? Is it mere coincidence that the creation story which churches emphasize is the one in which woman was created simply to help man while the creation story where woman is created as an equal alongside man is not?

So which story about the creation of Eve is supposed to be the "correct" one? The order and nature of events in these two Bible stories are contradictory and they cannot both be true, though they can both be false.

Is this a legitimate Bible contradiction or can the two Genesis accounts of when Eve was created be harmonized? If you think you can resolve this Bible contradiction, explain how — but your solution cannot add anything new that's not already in the stories and cannot leave out any details that the Bible provides.