  We present the discoveries of WISEA J041451.67-585456.7 and WISEA
J181006.18-101000.5, two low-temperature (1200$-$1400 K), high proper motion
T-type subdwarfs. Both objects were discovered via their high proper motion
($>$0.5 arcsec yr$^{-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 amongst 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] $\leq$ -1), making these objects likely the first
examples of extreme subdwarfs of the T spectral class (esdT). WISEA
J041451.67-585456.7 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.
