You cannot "think" yourself out of stress
It's true you can't "think" yourself out of stress but you can meditate on your stress, its effect on your body and your thinking, and come to terms with it in that way. Meditation does not involve thinking i.e., internal dialog, but it does involve taking the time to sit quietly for a half hour or more and just focusing on what exactly the"stress" is. That's the only way to achieve real understanding of it, to come to terms with it, to live with it, and to mitigate its negative effects. It's the same for other types of pain.
If, like most people, you deal with stress by trying not to think about it, by staying busy, by drinking, taking drugs, watching TV, even by exercising (alone) you'll still suffer from it.
If you want to see what meditation is about download a few lectures from audiodharma (to your smartphone or PC) and listen to them while commuting or before bed.
Meditation techniques are even taught in hospitals in the US thanks to unequivocal research showing its beneficial effects. See also books/audiobooks by Jack Kornfield, Lama Surya Das, the Dalai Lama, or Alan Watts among many.