I also didn't unlock the door (E) (picture 1) in my process, but if you just want to go back to the Uphill cave (C) you can follow below:
1. If you in door (D) area (picture 1) just go back through the door (D), and to the east entrance (picture 2), retreat the complex and leave underground.
2. If seem you are in door (A) area (picture 5), just go back through the door (A), and to the east entrance (picture 2), retreat the complex and leave underground.
Hope it can help you and not too complex.
