Does Genesis 2 Contradict Genesis 1?

Lots to say on this of course, but it's hard to imagine a better, wiser, more concise note on the relationship between the two creation accounts than what is offered in the ESV Study Bible:

Gen. 2:4–25 The Man and Woman in the Sanctuary of Eden. The panoramic view of creation in ch. 1 is immediately followed by a complementary account of the sixth day that zooms in on the creation of the human couple, who are placed in the garden of Eden. In style and content this section differs significantly from the previous one; it does not contradict anything in ch. 1, but as a literary flashback it supplies more detail about what was recorded in 1:27. The picture of a sovereign, transcendent deity is complemented by that of a God who is both immanent and personal. The two portrayals of God balance each other, together providing a truer and richer description of his nature than either does on its own. In a similar way, whereas ch. 1 emphasizes the regal character of human beings, ch. 2 highlights their priestly status.