"BAsed on that….how many calories do you think we would be burning??"
Dan,
According to the caloriesperhour.com algorithm for a 155# person hiking uphill with a pack weighing 21-40# you will burn 562 calories/hour. Multiply by number of hours you plan to hike/day to get a rough approximation of your daily calorie requirement. I assumed a pack weight of 21-40# based on the length of your trip making it unlikely you would be carrying less than 21#. My sense is that this is a minimum if you are going off trail, probably on talus part of the time, in the Sierra. I've done a lot of that down through the years and it is strenuous going at times. To do 10 miles/day would probably require at least 5 hours, given you will be carrying a heavier pack to begin with, for a calorie requirement of ~2800. If you have body fat to spare, it could supply part of that requirement, but remember you are going to have to spread it across 16 days.
If you carry 2300 calories/day, as Ben recommends, you should be prepared to make up a daily deficit of ~562 calories from body fat, which works out to ~9000 calories, or just under 3# of body fat. My personal experience during 4 trips of 15-17 days in the Sierra, on trail and off, all of which I lost significant weight on and once dangerously so, is that 2800 calories is well on the low side, especially for off trail travel with a heavy pack. I'd carry a minimum of 3000 calories/day just to be on the safe side and avoid the distinct possibility of having to come out early or end up feeling like s&!t 10 days or so into your trip. With a bit of care you can get 3000 calories down to 21 oz. I usually go in with 2800 @20 oz, so I know it can be done. That would give you a total food weight of 21# and some peace of mind in the bargain.
BTW, caloriesperhour.com is well worth spending some time on. They have a lot of information about these kinds of questions, including calorie content of various foods and other nutritional data. Another source well worth reading is Kevin Sawchuck's post on food in his writeup of his and Dave Chenault's experience on the Parcour de Wild last fall. You can locate it by using the BPL search function, and the food post is toward the end of the thread.
I hope this helps and, whatever you decide, I wish you all success.

