On the flight into STN, take an aisle seat at the front of the plane. Depending on the arrival gate, it may well be a 10+ min walk just to the immigration hall.
Once you exit arrivals at Stansted, turn right. About midway down the length of the terminal, the entrances to security screening start.
From arrival aircaft steps to departure gate, you're probably looking around 30 mins if you can run a bit and queues aren't too long. Worth looking at the airport map on the STN website in advance - signs are fairly good but helps to know a route in advance