Hi Zoubi!
Yes, this is possible. As long as you place the installations of UE 4.7 and 4.8 back into the expected location, when you hit the download button for them, assuming there hasn’t been any updates since the copy you still have, the Launcher will just run through the ‘Verifying’ stage and you’ll be ready to go.
For me, on windows with default install location, that means dropping the folders here:-
C:\Program Files\Epic Games\4.7
C:\Program Files\Epic Games\4.8
It might be different for you if you changed the location of the Launcher install.
Let us know if you need further assistance with the setup!