If you will be without power for 10 days, you will somehow need to make sure that your battery (batteries?) are kept up to charge . If you have 2 6v "golf cart type" batteries, that will help extend your stay but having just one 12v will not last 10 days for sure. If you have another 12v, why not pair them up in parallel so that you can at least get a few more amp hours from the two of them. Personally, I'd suggest getting a couple of 6v's if dry camping is something you will be doing again in the future.
If you have never dry camped before, you will need to be very frugal with your power needs - especially if you don't have a generator or solar panels to help out.
Run the water pump for short periods only and as little as possible. Take navy showers. In the evening, use as few lights as you can. If you are going to be doing more dry camping, invest in some LED lights. They consume about 1/10th the power of incandescents.
Remember, you will need some battery power at the end of the your stay to retract the slides. When putting your slides out, stay hooked up to your truck then unplug. When bringing them in, do the same thing.
If you have children along, talk them about what needs to happen to conserve both water and batteries. Everyone needs to make adjustments and learn about what you need to do differently than when you are hooked up to shore power.
I'd pull the fuses on everything that doesn't need to be running at night - stereo for example -- it has a backlight that draws power.
Enjoy your first dry camp and stay safe.
2008 Cougar 5th Wheel 27RKS
2005 2500 GMC Duramax