SSOLVE (Submillimeter Solar Observation Lunar Volatiles Experiment) will use submillimeter and terahertz receivers to investigate water in the lunar exosphere by observing strong transitions of H2O, OH, and HDO against the Sun as a backlight source. Submm-THz systems provide the high sensitivity needed to resolve the fundamental uncertainties of water vapor in the lunar exosphere: how much is there, where does it come from, how is it lost, does it exist primarily as water molecules or as hydroxyl radicals. SSOLVE will be developed for a landed platform to access the sky over the lander and to measure the variability of exospheric water with time of day. If an orbital platform is available instead, the identical design could be deployed for nadir viewing of gas transitions against thermal emission from the lunar surface to map water in the exosphere at all latitudes and local times. The total column abundance of water and free hydroxyl radicals over the Moon’s surface addresses the highly uncertain quantity of water group species in the atmosphere and its chemical form. The relative enrichment of deuterium is an important constraint on the delivery mechanism for water to the lunar surface, particularly if the column abundance is greater than the exobase limit, which would imply an indigenous source. Identifying or ruling out significant indigenous water in the current atmosphere will provide important insight into whether the lunar formation process incorporated significant primordial water. Measuring the abundance of water in the lunar atmosphere and determining whether it is indigenous or exogenous is essential to assessing the likely availability of water for in situ resource utilization (ISRU) of limited lunar water supplies. The development program for SSOLVE will leverage existing capabilities and designs at Goddard Space Flight Center, derived from extensive heritage in microwave systems for Earth atmosphere investigations, including the successful Earth-orbital IceCube cubesat to measure ice clouds in Earth's atmosphere. SSOLVE will use a heliostat to track the Sun regardless of lander orientation or leveling. Designs have already been developed for antenna and telescope assemblies, the mechanism, and internal calibration. Suitable receiver designs are available at TRL4-5 to serve as the front end for the 557 GHz H2O, 509 GHz HDO, and 2.5 THz OH receivers, with suitable digital spectrometer back-end designs already at high TRL. SSOLVE is a low-risk, high sensitivity, high reliability concept with potential for high scientific payoff.