I succeeded in installing my printer using sudo hp-setup. However, the scanner needs hp-plugin.
I did sudo hp-plugin, and got error messages. I installed the drivers provided by Solus, but now, I still can not install my scanner. So, how to install hp-plugin? I did read it is enough to install the printer, but that is just not true.

5 days later

From my setup spreadsheet:
Software Center Install HPLIP
Software Center Install HPLIP-DRIVERS
Software Center Install Python-distro
Terminal type hp-plugin
Terminal type hp-setup
Involves some rebooting. I would reboot between each stage.
Note: hp-setup might install the hp-plugin during the process as well. I am not sure. It does on Zorin.