The other end *should* terminate on the roof in a box if it's like the more recent trailers.
Unless you are going crazy with panels, the stock number 10 wire will do fine. You are coming down from the roof at 16 to 18 volts. With 160W of panels, that's at or below 10A. Number 10 is one miliohm per foot. If you have a 40' round trip, that's 0.04 ohms. At 10A you will have a drop of 0.4V. Out of your 16V, that's 2.5% at full load. At lower loads, the loss will be less. Maximum rating wise, number 10 is generally considered to be good for 30A.
Since you don't have a controller yet, if you *are* going crazy with panels, run them in series / parallel. ( or get panels that put out 32 to 36V). Then your current is halved for the same power output. Something like a Victron MPPT 75 or 100 unit will be perfectly happy with the higher voltage input.