i had same issue i finally had time to fix it in my case i did the next :
- close the launcher , and make sure its not running from TaskManager
- edit DefaultEngine.ini from inside launcher install directory (in my case its in C:\Program Files\Epic Games\Launcher\Portal\Config\DefaultEngine.ini) open it then under [http] remove HttpTotalTimeout=30 line (open notepad as admin so you can save )
now open epic game launcher you should be able to download engines
from my understanding this was renamed from HttpTimeout to HttpTotalTimeout when launcher tries to download the manifest files which is 100+ MB each! and your internet slow it will Timeout in 30 seconds before the download finish and you will get the error