We present near-infrared spectroscopic observations (0.8--2.5 ¿m) of E-type asteroids. We combine these observations with visible wavelength spectra obtained by other researchers and perform Hapke theory mixing model simulations of E-type asteroid spectra in order to constrain possible compositions. Aubrites were originally suggested as the meteorite analog for the E-type asteroids because of their similar visible wavelength colors and high albedos. The designation E was originally linked with the mineral enstatite, common in aubrite meteorites. More recently, the sulfides troilite and oldhamite have been suggested as possible components of E-type asteroids. We tested the suggested compositional interpretations of aubrite meteorites and/or aubrites enhanced with sulfides. We also tested compositions of aubrites mixed with low-iron silicate minerals. We find that E types can be separated into three groups on the basis of inferred composition: Nysa-like E types are consistent with silicate mineralogy higher in iron than the mineral enstatite; Angelina-like asteroids are consistent with silicate mineralogy, including a sulfide such as oldhamite; and Hungaria-like E types are not inconsistent with aubrites. Our results indicate that some E-type asteroids may be composed of materials that are not sampled by meteorites.