I am surprised that the Romex would be the 12 volt
power source. But again nothing surprises me with these old rigs.
When you disconnected and removed the old radio. Was it connected to the Romex?
If so, it's probably a safe bet that it is 12 volts. BUT I WOULD CHECK IT WITH A METER TO MAKE ABSOLUTELY SURE.
If it is 12 volts. My guess would be that BLACK IS POSITIVE and WHITE IS NEGATIVE. But I would check to make sure. If this is the case, the positive (red) wire of the radio would connect to the black wire (thru a properly sized fuse). The white wire from the Romex would then be connected to the metal chassis of the radio. There is probably a stud with a nut on it. Which may be part of the mounting hardware.
The speakers in my trailer are mounted on the bottom of the overhead compartment in the berthing area. Look for wires in the overhead compartments.
I would take a real close look in the box the old radio was mounted and see if among the speaker wires there is a single black stranded wire. If so, I'd bet that's the +12 volts you are looking for.
Don't know what you paid for the new radio, but they don't like being connected incorrectly. So be certain that the polarity and voltage are correct before connecting it. Also make sure there is a fuse on the +12 volts