How long should i jog for burning calories?

i over ate about 1100 calories today (i ate about 2500) and d planning on going for a jog. how long should i jog for and what would be most effective? i am 5'7 120 pounds and just got out of the hospital with purging anorexia. my dietition at the hospital told me i need to be eating about 2500 calories a day but i need to excersise i can't eat this much!