It's a simple wiring. Just take the wires from the solar panel
to the charge controller. Then take wires from the charge controller to the battery.
The charge controller will know when the battery needs to be charged and keeps the juice from flowing the other way, that is back to the panel. So, when on 110 the battery should be charged by the convertor and the charge controller will know that the battery doesn't need any juice from the solar panel, that is unless your convertor is failing to charge the battery.