Barring any medical issue that complicates things, yep. Exercise to use the calories you take in.

Backpacking is excellent exercise.

"Picky eating" is one thing - not getting the nutrients your body needs to stay in balance is another. A chat with a dietician or nutritionist (not a doctor) might be helpful in rewriting your expectation that you can lose weight without eating good healthy veggies and fruits. Without meats, veggies and fruits, you are left with starches, carbs and other things that are okay in moderation but are not a healthy diet all on their own. You aren't getting everything you need if you're skimping on the veggies.

And proper hydration is another HUGE key to maintaining healthy body weight - you don't have a properly functioning "engine" without it.