We present the discovery of two nearby L dwarfs from our 2MASS proper motion search, which uses multi-epoch 2MASS observations covering ~4700 square degrees of sky. 2MASS J18212815+1414010 and 2MASS J21481628+4003593 were overlooked by earlier surveys due to their faint optical magnitudes and their proximity to the Galactic Plane (10 degrees < |b| < 15 degrees). Assuming that both dwarfs are single, we derive spectrophotometric distances of ~10 pc, thus increasing the number of known L dwarfs within 10 pc to 10. In the near-infrared, 2MASS J21481628+4003593 shows a triangular-shaped H-band spectrum, strong CO absorption, and a markedly red J-Ks color (2.38+/-0.06) for its L6 optical spectral type. 2MASS J18212815+1414010 also shows a triangular-shaped H-band spectrum and a slightly red J-Ks color (1.78+/-0.05) for its L4.5 optical spectral type. Both objects show strong silicate absorption at 9-11 microns. Cumulatively, these features imply an unusually dusty photosphere for both of these objects. We examine several scenarios to explain the underlying cause for their enhanced dust content and find that a metal-rich atmosphere or a low-surface gravity are consistent with these results. 2MASS J18212815+1414010 may be young (and therefore have a low-surface gravity) based on its low tangential velocity of 10 km/s. On the other hand, 2MASS J21481628+4003593 has a high tangential velocity of 62 km/s and is therefore likely old. Hence, high metallicity and low-surface gravity may lead to similar effects.
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