Although T Tauri is one of the most studied young objects in astronomy, the nature of its circumstellar environment remains elusive, due in part to the small angular separation of its three components (North-South and South a-b are separated by 0.68'' and 0.12'', respectively). Taking advantage of incredibly stable, high Strehl ratio point-spread functions (PSFs) obtained with mid-IR adaptive optics at the 6.5 m MMT, we are able to resolve the system on and off the 10 μm silicate dust feature (8.7, 10.55, and 11.86 μm; 10% bandwidth), and broad N. At these wavelengths, South a-b are separated by only ~0.3λ/D. This paper describes a robust Markov chain Monte Carlo technique to separate all three components astrometrically and photometrically, for the first time, in the mid-IR. Our results show that the silicate feature previously observed in the unresolved T Tau South binary is dominated by T Tau Sa's absorption, while Sb does not appear to have a significant feature. This suggests that a large circumbinary disk around Sa-Sb is not likely the primary source of cool dust in our line of sight, and that T Tau Sa is enshrouded by a nearly edge-on circumstellar disk. Surprisingly, T Tau Sb does not appear to have a similarly oriented disk.