I keep getting this message: Screenshot by Lightshot
Double check in your control panel > uninstall software that UE4 isn’t listed there, if it is, try to uninstall it. Also have you rebooted between installation attempts?
Hi Spectro87,
Once you try Card and Dungeon’s suggestion above, if the issue persists, try the suggestions here.
If that still doesn’t fix the issue, make sure to post the EpicGamesInstallerLogs that is described in that section and post a copy of your Dxdiag (system specs).
I had installed UE4 for a game demo previously and I guess this was preventing the Epic Games Launcher from installing. Everything works now. Thanks. 
Glad to hear it, always nice when issues get solved!