from what I am
reading, this outlet on the side is only a 12V connector that is wired direct (hopefully with fuses) to the battery. If there was a solar controller inside your RV it would be mounted on a cabinet or wall so you could see it. What this solar controller does is act like a voltage regulator so you don't over charge your batteries.
Now 10A rating is not much. depending how far south you are using this, a single 100W panel might put out 4-7 amps.
If your going to go portable I would recommend a 20A controller because it gives you more overhead and don't cost much different than 10A controller.
Many suite case panels come with the charger built in, but they are also available separately for around $20 bucks on amazon if your going to try to use a larger 12v panel.
That connector on the RV might be an "odd ball", and to buy
equipment that matches the connector might cost 2X more than equipment that uses standard connectors, but a
dapters are available on Amazon. Also Check the connector on RV with volt meter before using it as I have heard some are wired backwards compared to the industry standards.
NOTE: another thing that is great about solar is you can also use it during storage to keep your battery fully charged (if your storing in a safe location). I use a single 100W panel to keep Three 27 series batteries fully charged in storage.