eopkg
is the command to install software packaged for Solus (basically files with a .eopkg extenstion). You can't use it to install random things that haven't been packaged.
When a software is not in the repository, it's advised to search if it's available as a snap
, flatpak
or eventually appimage
universal package, but bad luck for you, I don't think XFburn is available as universal package as well. This software is actually an application of the XFCE desktop environment that is not supported on Solus.
So your only option is to build it from source. The official repository is here. It might eventually requires dependencies that are not in the solus repository (to be checked).
My advise is to use a similar application that is available in the repository (like brasero
for example).
PS: Don't mix different issues/questions in the same topic please.