Vitamin E does combine with oxygen which is beneficial to polyunsaturated fats and vitamin A . Both polyunsaturated oils and vitamin A combine with oxygen and break down. Vitamin E interferes with that break down process. Because of its antioxidant properties, vitamin E is stable to most cooking methods except long cooking at very high temperatures that would break down fat as well. Vitamin E deficiency has not been proven in humans, but it has in animals.
Vitamin E is so widespread in foods that it is difficult to produce a deficiency in humans.
Also, because it can be stored in the body, it is difficult to produce a deficiency. I suppose it would be possible to induce a vitamin E deficiency by eating an extremely low fat diet for a prolonged period of time. Other fat soluble vitamin deficiencies would also appear though.