Why does Gilgamesh leave Uruk after Enkidu's death?

He is trying to avoid being killed himself Gilgamesh leaves Uruk to 'wander the wild" for two reasons. One is that he is grief stricken at the death of Enkidu and that this is a way of expressing his sorrow. This is explained in tablet ten where Gilgamesh is asked three times why his appearance and features are so haggard and why he has journeyed so far from civilization.

Each time he recounts his former exploits with Enkidu and the overwhelming sense of loss and dejection he has experienced since his friend's death. The second reason is that Gilgamesh is fearful of his own death. The purpose of his journey to the ends of the earth is to find Utnapishtim, the immortal survivor of a great flood that destroyed all living things.

Gilgamesh hopes to force the flood hero to share the secret of his immortality, and so escape the fate of Enkidu.

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