Most people will burn between 340 to 370 calories per hour of hiking or walking depending on the person weight.
So for a hike of 10 miles you should burn off as many as 820 to 850 calories when hiking or walking 10 miles.
Hiking 10 miles will take you around 2 hours and 30 minutes to around 3 hours depending on how fast you walk or hike and how often and how long you take breaks and rest.
So you might burn 850 calories even as much as 1,000 calories in a 10 mile hike and then if you hike one way 10 miles and then the next day or so hike the 10 miles back then you'd burn off an additional 850 to possibly another 1,000 calories.
So you certainly can lose quite a bit of weight hiking 10 miles and hiking is a good exercise to keep your body active, healthy and get you out there into nature and having fun.