Basic medical science has proven repeatedly that taking in fewer calories than you burn in a day will result in weight loss. Exercise is not necessary at all to lose weight and keep it off. You burn calories just sitting on your ass all day. As long as you eat below that amount, you will lose weight.
It also has nothing to do with what you eat. You can gain weight eating a diet of nothing but boiled chicken and steamed broccoli if you eat too much of it every day. And you can lose weight eating nothing but deep fried ice cream if you eat too little of it every day. The science is in. The point is well-known and proven.
I can't believe anyone feels a need to argue about this. Facts are facts, now shut the hell up.