A,B,C and D points are given, how can I calculate the E point? I know this method, but I would like to know if there is any other solution exists, that does not need the equalation of both lines.
Maybe there is some trick using Pythagorean theorem or Intercept theorem or anything else.
Thank you for any advice!

Hint: Use Thales' Theorem, e.g. in the triangle A0B with E