Recently, the neutron star X-ray binary EXO 0748-676 underwent a transition to quiescence. We analysed an XMM-Newton observation of this source in quiescence, where we fitted the spectrum with two different neutron star atmosphere models. From the fits we constrained the allowed parameter space in the mass-radius diagram for this source for an assumed range of distances to the system. Comparing the results with different neutron star equations of state, we constrained the distance to EXO 0748-676. We found that strange quark matter equation of state is consistent with the mass and radius from our fits only if EXO 0748-676 is at a distance of less than 5 kpc, whereas the normal neutron star equation of state is consistent with our best-fitti...