This is a very difficult question to answer, because how many calories you'll burn, and how hard you'll be working, varies with the intensity of the session and that will be influenced by terrain, wind etc as well as how hard you push and how heavy you are.

However, I can give you some idea. I'm a big rider at around 200lbs. If I put out about 200 watts I will burn around 11 or 12 calories per minute. On my own, on a flat road, with little or no wind, at 200 watts I will be travelling at about 20mph. So at that level of effort, I'll go through around 700 calories per hour, with my heart rate somewhere in the 140s.

But that's just me. Your numbers will be different, and flat roads with little or no wind may be hard to come by

Essentially, you can't ride hard enough to lose significant weight in just 10 miles. If you want your cycling to contribute towards weight loss, you need to ride for longer. And doing so will build your aerobic fitness, of course.