We present an X-ray spectral and timing analysis of two $NuSTAR$ observations of the transient Be X-ray binary SAX J2103.5+4545 during its April 2016 outburst, which was characterized by the highest flux since $NuSTAR$s launch. These observations provide detailed hard X-ray spectra of this source during its bright precursor flare and subsequent fainter regular outburst for the first time. In this work, we model the phase-averaged spectra for these observations with a negative and positive power law with an exponential cut-off (NPEX) model and compare the pulse profiles at different flux states. We found that the broad-band pulse profile changes from a three peaked pulse in the first observation to a two peaked pulse in the second observation, and that each of the pulse peaks has some energy dependence. We also perform pulse-phase spectroscopy and fit phase-resolved spectra with NPEX to evaluate how spectral parameters change with pulse phase. We find that while the continuum parameters are mostly constant with pulse phase, a weak absorption feature at ~12 keV that might, with further study, be classified as a cyclotron line, does show strong pulse phase dependence.
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