I removed torbrowser-launcher, removed the TorBrowser or torbrowser folder from the /home/<user>/.config folder, downloaded the Linux download from the Tor site, extracted to a folder under my home folder, and Tor browser is working again for me under Solus.
I use the Openbox window manager, so I just had to edit the entry in the Openbox menu GUI to point to the start_tor_browser file under the tor-browser_en-US/Browser folder. If you're using Gnome, Budgie, or Mate, you'll probably need to use the start-tor-browser.Desktop file. There are two start-tor-browser.Desktop files, so I'm not sure which one you should use.