From: The Domesticated Brain by Bruce Hood.
Feelings and emotions are two sides of the same coin. Emotions are short-lived, outward responses to an event that everyone around can read, like a sudden burst of anger or fit of laughing, but feelings are the internal lingering experiences that are not always for public consumption. We can have feelings without expressing them as emotions. They are part of our internal mental life. Without feelings, we would not be motivated to do the things we do. Feelings we get from others are some of the strongest motivation that we can have. Without feelings, there would be no point getting out of bed in the morning. Even pure logic needs feelings. When se solve a puzzle, it is not enough to know the answer. You have to feel good about it too. Why else would we bother?