How can I install an app which has .deb extension?

The .deb extension is for Debian and its derivatives, and so it can not be installed in Solus. Solus uses eopkg for package management. You may want to see if the application in question is available as a Flatpak or Snap. Otherwise, you can make a package request. See https://getsol.us/articles/packaging/submitting-a-package/en/ for more information.

    Besides having an internet name I have coveted for a long time, I'd like to add to beerminer 's excellent reply.
    If you don't feel like snap/flat (I trust neither but most do) or submitting a request (this has worked for me twice) then you will ALWAYS find something comparable that you can love that replaces the app from your last operating system--if you just try it. 2 cents.