How can I successfully run away from stress?

Keep running. I assume you are using running to help relieve stress i have run for 40 years and find it helpful. I would suggest running at a comfortable pace at least 20-30 minutes and perhaps listen to some mellow music to help calm yourself.I believe it will help relieve stress and hope you could do it 3-5 times per week.
Can't; learn to deal. Can't run away from stress; can learn to decrease stress when possible, e.g. Work, home, health, relationships, money issues. Sometimes, that can't be decreased, so need to learn better ways to deal with it. Can include "centering" techniques, e.g. Meditation, to take the edge off; can include behavioral or "cognitive" therapy to increase insight, come up with different responses to the stres t.