Ok, please check the previous post...I corrected it as to the battery info...I must have been near zombie mode when I hit/read the link cause I swear I thought it said 6 volts.
Your power demands: I checked the Engle site, it appears the unit draws 2.5 amps per hour. For a full day the power demand would be 2.5 x 24 (hours), or 60 amps, assuming the unit ran all the time, they typically cycle on/off to regulate temps, but this is worst case and provides a reserve.
Running a 1.5 amp fan, say from 10pm to 6am (8hours); would draw 12 amps.
Lighting, let's just say 2 amps for 5 hours; 10 amps. Total current demands are 82 amps over 24 hours (worst case), you might get by with a bit less...but for planning, it is better to figure worst case, cause we all lie about how much juice we use.
Power supply: 4 15 watt solar panels...output (in the ideal world) would be 60 watts (amp output is watts divided by 12 volts=5 amps)...your actual output will be about half that typically at best (clouds, sun at angle, heat loss). This is about 5 amps/hr.(ideal). So lets say a good day gives you 8 hours of sun, figure 3 amps/hr averaged output (real life)= 24 amps back into battery in a good day.
You put 24 amps back in to the battery on a good day...so, without a external source of additional charging power, your running a deficit of 58 amps over 24 hours....you need to bridge this deficit with more input amps (higher rated solar panel(s), alternator charging from vehicle or a generator/charger), or of course, less amp demands.
The system you initially mentioned with one of these batteries would get you thru the first night out, figuring it was charging off the alternator as you drove...OK, but your battery would be down in the AM and absent supplemental charging, by day two, your out of juice.
Play with your "energy budget", and figure your amp needs over 24 hours...figure your solar output in real world numbers, of any other available charging input systems, and think of your battery as a glass of amps you never want to draw down more than 40%...and you'll be on your way.