We report new spectral and temporal observations of the magnetar 1E 1841 - 045 in the Kes 73 supernova remnant obtained with the Nuclear Spectroscopic Telescope Array ( NuSTAR ) . Combined with new Swift and archival XMM-Newton and Chandra observations , the phase-averaged spectrum is well characterized by a blackbody plus double power-law model , in agreement with previous , multi-mission X-ray results . However , we are unable to reproduce the spectral results reported using Suzaku observations . The pulsed fraction of the source is found to increase with photon energy . The measured rms pulsed fraction is \sim 12 % and \sim 17 % at \sim 20 keV and \sim 50 keV , respectively . We detect a new feature in the 24–35 keV band pulse profile that is uniquely double-peaked . This feature may be associated with a possible absorption or emission feature in the phase-resolved spectrum . We fit the X-ray data using the recently developed electron-positron outflow model of Beloborodov ( 3 ) for the hard X-ray emission from magnetars . This produces a satisfactory fit allowing a constraint on the angle between the rotation and magnetic axes of the neutron star of \sim 20 ^ { \circ } and on the angle between the rotation axis and line-of-sight of \sim 50 ^ { \circ } . In this model , the soft X-ray component is inconsistent with a single blackbody ; adding a second blackbody or a power-law component fits the data . The two-blackbody interpretation suggests a hot spot of temperature kT \approx 0.9 keV occupying \sim 1 % of the stellar surface .