I'm posting a link to a caloric calculator from bodybuilding .... it should translate very well to any intense level of exercise such as backpacking.
You can vary this number by 20% ... 20% more, with adequate protein intake, will build muscle. 20% less, with adequate protein and nutrition, will result in fat loss with a little muscle loss.
As a side note: one gram of protein intake per pound of lean body mass would be key to not burning muscle on a long hike.
So ... if you are of average fitness, burn an average of 450 calories per hour of intense exercise, and hike 10 hours a day, you'd need 4500 calories per day to maintain your current body mass. Drop that to below 3500 calories and your in starvation mode ... which means being tired and lathargic all the time. Of course, your BMR plays a role in all of this as well.
3500 calories, divided by 120 calories per ounce of food yields 29 ounces of food per day (about 2 lbs).
In the short term you can fool your body into not kicking into starvation mode by using methods like the caloric drip method and maintaining an almost constant stream of nutrition during the day.
Whatever method you chose, however, you must realize that 20 ounces of food per day, times an average of 120 calories per ounce, yields 2400 calories. 2400 calories when your burning 4500 calories per day gives you a 2100 calorie per day deficit. One pound is 3500 calories, so this is more than half a pound of body mass loss per day.
On a long hike, not many people can stand 3.5 lbs per week of body mass loss ... that's 15 to 20 lbs per month ... and that's assuming that you have enough protein intake to keep your body from burning muscle ... which burns easier than fat.
Of course ... if your 160 lbs and 20 years old with 15% body fat, your body is much more forgiving of what you put into it. That changes with age.
Nutrition is huge, at least for us old dogs.