Hmm, I’m not seeing anything there. Thanks for sending that though.
Next maybe try Verifying the engine. You can click the yellow arrow on the Launcher version to do that.
If that doesn’t work, try navigating to the UE4Editor.exe directly and see if it will open that way. This will help us determine if the Launcher is blocking it from opening. Your file path should be similar to this:
drive:\Program Files (x86)\Epic Games\4.14\Engine\Binaries\Win64\UE4Editor.exe