Soil moisture is closely related to the surface temperature (Ts) and fractional vegetation cover(Fr). Ts is estimated from the infrared sensors onboard LandSat. Fr is calculated as the square of NVDI (the Normalized Difference Vegetation Index).
Soil moisture is not determined analytically as a function of Ts and Fr. Instead, it is estimated by a precalculated corresponding relationship between soil moisture and paired Ts and Fr.
Perhaps this paper could answer your question in detail. Article Using Landsat and NOAA Satellites on Soil Moisture Mapping a...