Patrunjelu: I have not had luck in getting it to run on its own, but I did manage to get it to run using DxWnd which is a nifty tool that forces games to run in windowed mode (among other stuff). Screenshot of the game in action (screen res is 3200x1800):
http://imgur.com/RtheCVO Steps:
1. Download DxWnd from
https://sourceforge.net/projects/dxwnd/
2. Run dxwnd.exe as administrator, click Edit > Add
3. In the Main tab enter the Name of the game and its Path (browse to the .exe).
4. At the bottom of the window you will see "Window initial position and size"; change those so that the window is not too small for you. If you change the option X, Y coordinates (right side) to Desktop Working Area, the game will fill up the desktop minus the start bar which is pretty handy if that's what you want.
5. Go to the Input tab and in the top left corner set Cursor Clipper to LOCKED. This will lock the cursor to the window so you can scroll the map in the game using your mouse.
6. Press the Try button (bottom of window). If the game runs ok and you're happy, press Ok to save it. Once it gets in DxWnd's main list, double click its entry (the one with the green orb), and the game will run.
There are many options in DxWnd but with the above I found I can play just fine. Feel free to experiment.
This is, hands down, the best advice for the annoying black screen issue when opening EDMW in Windows 10. I tried all other solutions in this page, and left this one for last.
I have two paid for copies of the game, the one that finally worked with this tip, is not the GOG one but the one I had bought last year in Old-Games.
Thanks, thanks and thanks again.