Obviously exercise will increase the number of calories you burn but also strength exercises (weights etc) are crucial to increasing or maintaining your muscle mass to ensure that you can still carry out basic everyday tasks. I only say this because if you are only dieting (and not exercising) then you are reducing/not able to maintain your muscle mass. It is also important to have muscle mass so that you still burn calories while you are resting. If you were to diet alone you would need to reduce your calorie intake even more to retain muscle mass. However, you do not want to eat so little that it has negative health consequences, we want to make ourselves healthy people, not ill!!
This is why you want the combination of exercise and a healthy diet, it's the best way to go. Personally I am going to aim for 1500 calories a day and going to the gym 4 times a week.
Not only does exercise make you feel good, improve your social life (I need a gym buddy or two!) and improve mental health but it also prevents the development of diseases. It has been shown that there is a link between inactivity and the risk of metabolic conditions, cardiovascular diseases, pulmonary diseases, cancers, neurological problems, reduced quality of life and shorter life expectancy. If that's not enough to make you exercise then I don't know what is!
Again dieting alone rarely will have a positive impact on your life. It won't really positively impact your mood (you will be left hungry!), anxiety will increase and it won't have a positive impact on your social life (you will always be worrying about what you could possibly eat). I must say, I really feel like this is true, certainly for me anyway. I do have a slight panic when I have to go our to eat as I am quite a fussy eater so finding something to eat is almost like a chore! This will then increase my anxiety which is never a good feeling and I'll be in a bad mood! So that is why I want to get back to the gym so I can enjoy myself when I want to go out for dinner with friends.
I got the information from this website, well worth a read (though I feel as if what I have written makes it easier to understand), it's a good one.