A method is presented for retrieving temperature and composition from 150-350 km in Earth’s thermosphere using total number density measurements made via EUV solar occultations by the PROBA2/LYRA instrument. Systematic and random uncertainties are calculated and found to be less than 5% for the temperature measurements and 5-20% for the composition measurements. Regression coefficients relating both temperature and the [O]/[N2] abundance ratio with EUV irradiance at 150, 275 and 350 km are reported. Additionally, it is shown that the altitude where [O] equals [N2] decreases with increasing solar EUV irradiance, an effect attributed to thermal expansion. Temperatures from 2010 to 2017 are compared with estimates from the MSIS empirical model and show good agreement at the dawn terminator but LYRA is markedly cooler at the dusk terminator, with the MSIS-LYRA temperature difference increasing with solar activity. Anthropogenic cooling can explain this discrepancy at periods of lower solar activity, but the divergence of temperature with increasing solar activity remains unexplained. LYRA measurements of the exospheric sensitivity to EUV irradiance are compared with contemporaneous measurements made at Mars, showing that the exospheric temperature at Mars is approximately half as sensitive to EUV variability as that of Earth.