\pi Men c was recently announced as the first confirmed exoplanet from the TESS mission . The planet has a radius of just 2 R _ { \oplus } and it transits a nearby Sun-like star of naked-eye brightness , making it the ideal target for atmospheric characterisation of a super-Earth . Here we analyse archival ROSAT and Swift observations of \pi Men in order to determine the X-ray and extreme-ultraviolet irradiation of the planetary atmosphere and assess whether atmospheric escape is likely to be on-going . We find that \pi Men has a similar level of X-ray emission to the Sun , with L _ { X } / L _ { bol } = ( 4.84 ^ { +0.92 } _ { -0.84 } ) \times 10 ^ { -7 } . However , due to its small orbital separation , the high-energy irradiation of the super-Earth is around 2000 times stronger than suffered by the Earth . We show that this is sufficient to drive atmospheric escape at a rate greater than that readily detected from the warm Neptune GJ 436b . Furthermore , we estimate \pi Men to be four times brighter at Ly \alpha than GJ 436 . Given the small atmospheric scale heights of super-Earths , together with their potentially cloudy atmospheres , and the consequent difficulty in measuring transmission spectra , we conclude that ultraviolet absorption by material escaping \pi Men c presents the best opportunity currently to determine the atmospheric composition of a super-Earth .