  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
~12% and ~17% at ~20 keV and ~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 (2013) 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 ~20
degrees and on the angle between the rotation axis and line-of-sight of ~50
degrees. 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~0.9 keV
occupying ~1% of the stellar surface.
