We discuss recent Chandra and XMM-Newton observations of the bright isolated neutron star RX J1856.5 - 3754 and suggest that the absence of any line features is due to effects of a high magnetic field strength ( \sim 10 ^ { 13 } G ) . Using different models for the temperature distribution across the neutron star surface assuming blackbody emission to fit the optical and X-ray spectrum and we derive a conservative lower limit of the ” apparent “ neutron star radius of 16.5 km \times ( d/117 pc ) . This corresponds to the radius for the ” true “ ( de-redshifted ) radius of 14 km for a 1.4 M _ { \odot } neutron star , indicating a stiff equation of state at high densities . A comparison of the result with mass-radius diagrams shows that quark stars and neutron stars with quark matter cores can be ruled out with high confidence .