See my other comment, but exercise can be a critical way that people both lose weight and maintain weight loss. Losing weight is relatively easy, but maintaining it is hard, and exercise can be critical to the latter.
You need to stop thinking about exercise as burning calories. Exercise can be critical in getting hormones, particularly leptin, back to a normal function. Exercise, particularly weightlifting, can help build muscle and prevent muscle loss from losing weight.
Eating less is not the secret. That's to reductionist.
The secret is altering your energy balance.
You can alter your energy balance from a combination of diet and exercise, and the way you handle both will further impact your energy balance. Your hormones will also play a critical role in your ability to maintain this as well.
Getting good sleep will also be critical for altering this energy balance and setting yourself up for weight loss. People who don't get 7-9 hours of sleep a night aren't going to be producing enough human growth hormone at night, and they won't be able to recover from exercise or build lean tissue.
I would never, ever recommend someone try to lose any significant amount of weight without weightlifting. It's a fool's errand.
Yes, you'll lose the weight by eating less, and in the process you may end up having half of that weight loss be muscle mass. Now your metabolic rate is in the gutter, and you have set yourself up perfectly for a rebound in weight.
If you want longterm weight loss, exercise and eat well. Try to get at least 10,000 steps a day and then aim for 4-6 days a week of strenuous exercise.