Download the source files.
Unpack the archive and - opening a terminal in the resulting folder:
To get a launcher available:
and paste this:
Name=Exaile Music Player
Exec=sh -c "/usr/local/bin/exaile"
Make it executable (
chmod +x ~/.local/share/applications/exaile.desktop) or trust it when prompted by Nautilus file manager.
Tested this in Solus 3.999, without the problems encountered in Ubuntu.
python-dbus was already installed,
python-gi-cairo was not needed.