Vitamin E is very popular among the beauty community nowadays due to the benefits it has shown in terms of overall skin health. For skin care it is applied topically. Many people even recommend it as an anti-aging treatment. Although there's not a conclusive research that has proven Vitamin E's efficiency in treating dark spots. Since it is easily available OTC in oral as well as topical form, it makes it a go to remedy for most people.
It is best to apply Vitamin E and leave it overnight to experience the maximum benefits through the absorption. In the day time the problem is that you might have to put your make up on and other skin care products, which might be a bit hard to do if you already have Vitamin E on your face. That's why leaving it overnight works the best, especially if you're looking to get rid of dark spots from your face. However if you're looking to remove dark spots from legs, there's other better remedies out there.
Overall Vitamin E might not be the best choice for treating dark spots, although it is rich in antioxidants and is still helpful in delaying wrinkles etc. For dark spots specifically, most people generally go with Vitamin A based solutions because of its proven effectiveness in lightening the skin.