Can you try closing the launcher program, then on the shortcut (start menu CRYENGINE Launcher) right-click and select run as administrator. Try to open the editor again, you can use the cog wheel and select launch editor also.
If this does not work then in the cryengine launcher go to "Library" -> "My Engines" -> under the green down down box select "Reveal in Explorer".
In the new explorer open the folder "bin" then "win_x64" and launch the program "sandbox.exe" in this folder.
Please give as much info as you can regarding these procedures, what happens etc.
there should be an editor.log file created in the main engine folder.
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