Unity doesn't support 19.10 only 18.04 at the moment. But to get it working 19.10 you need to download UnityHub, but there is also flatpak as well (which seems to be fine).
sudo apt install libgtk2.0-0:i386
If you don't have it, it won't open for some reason. But if you open from terminal, it will give you some errors which lead me to this link : error while loading shared libraries: libgtk-x11-2.0.so.0: No such file or directory
You'll probably get some blank error messages in the console.
Add this line
deb http://security.ubuntu.com/ubuntu xenial-security main
at the end of
/etc/apt/sources.listfile (source). Then
sudo apt update && sudo apt upgrade -y && sudo apt install libssl1.0
I think you need install it, I can't actually remember, maybe just update/upgrade is enough
You will probably get some burst compiler errors, so just install
sudo apt install libncurses5
and you are off to the races, as said from this link
There are also other issues with Unity in Linux but so far, these are main ones to get you up and running.
Also visit the Linux Editor forum, there are lot of people there reporting/solving issues. But also most importantly, report issues official to Unity. Its the only way to Linux editor will get better.
The Unity3D folks don't make it easy to find Linux install files.