From the website it seems to suggest those two commands and I installed it recently and it worked fine (I don't think I got an icon though, i just kept booting it with ./electrum)
sudo apt-get install python3-setuptools python3-pip
python3 -m pip install --user Electrum-3.3.8.tar.gz[fast]
This thinks your version of electrum is already installed:
Successfully built Electrum
Installing collected packages: Electrum
Found existing installation: Electrum 3.3.8
Uninstalling Electrum-3.3.8:
Successfully uninstalled Electrum-3.3.8
Successfully installed Electrum-3.3.8
I'm guessing there's a catch somewhere that's suggesting it's already installed and stopping the program from running.
I tried the option "Run without installing" on the Electrum web site - worked perfectly.
Probably won't be a dependency issue,
If you run it again and still don't get anywhere, I'd suggest trying to install the appimage instead.