Earlier quoted context omitted.
You can access the source code to unreal engine when you get a license, but the terms are not by any stretch of the imagination open source. You wouldn't be able to freely share your modifications for instance.
> You wouldn't be able to freely share your modifications for instance. Have you read the unreal engine license agreement? [0]. Section 3.a covers modifications [0] https://www.unrealengine.com/en-US/eula/unreal
Edit: I see some language covering this further up.