We present the discoveries of WISEAJ041451.67-585456.7 and WISEAJ181006.18-101000.5, two low-temperature (1200-1400K), high proper motion T-type subdwarfs. Both objects were discovered via their high proper motion (>0.5yr^-1^); WISEA J181006.18-101000.5 as part of the NEOWISE proper motion survey and WISEA J041451.67-585456.7 as part of the citizen science project Backyard Worlds; Planet 9. We have confirmed both as brown dwarfs with follow-up near-infrared spectroscopy. Their spectra and near-infrared colors are unique among known brown dwarfs, with some colors consistent with L-type brown dwarfs and other colors resembling those of the latest-type T dwarfs. While no forward model consistently reproduces the features seen in their near-infrared spectra, the closest matches suggest very low metallicities ([Fe/H]<=-1), making these objects likely the first examples of extreme subdwarfs of the T spectral class (esdT). WISEAJ041451.67-585456.7 and WISEA J181006.18-101000.5 are found to be part of a small population of objects that occupy the "substellar transition zone", and have the lowest masses and effective temperatures of all objects in this group.