As activity in Earth orbit continues to grow, it is important to characterize the environment of near‐Earth space. One means of remotely sensing lower thermospheric neutrals is by measurement of O and N2 density through the observation of far‐ultraviolet (FUV) airglow of atomic oxygen at 135.6 nm and the N2 Lyman‐Birge‐Hopfield (LBH) bands (~130–180 nm), as has been done on the Ionospheric Connection Explorer (ICON), Global‐scale Observations of the Limb and Disk (GOLD), and Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) missions. This technique is not without limitations, however, as the FUV measurements suffer from contamination by ionospheric emissions at low latitudes and auroral emissions excited by precipitating energetic electrons and protons at high latitudes. Previous work has shown the potential for making measurements of O and N2 density in the lower‐middle thermosphere using observations of extreme‐ultraviolet (EUV) airglow. This measurement approach has a potential advantage in that it does not have an inherent ionospheric emission that must be accounted for. Additionally, these emissions are primarily excited directly by solar UV rather than electron impact and thus have the potential to enable expansion of neutral density observations into the auroral zone and polar cap where the FUV measurement cannot be applied. This article demonstrates a new approach and algorithm designed to retrieve thermospheric O and N2 density from 150 to 400 km using measurements from the ICON EUV instrument. The retrieval results throughout 2020 are summarized and compared to measurements from ICON FUV, GOLD, and SWARM. Plain Language Summary The region of space where most satellites orbit is almost empty ‐ but not completely empty. The small amount of nitrogen and oxygen gas present can cause satellites to gradually fall out of orbit through drag. A failure to understand and evaluate changes in the density of the upper atmosphere led to the loss of 38 Starlink satellites in February 2022, for example, This is one reason that it is important to understand how much gas is in near‐Earth space and how the amount changes over time, but orbit decay due to drag makes it difficult to make direct measurements. One common solution is to measure the amount of gas from afar, taking advantage of the fact that these gases emit small amounts of light in the far‐UV spectrum. There are some limitations to this approach, one of which being that charged particles in the same region can create an extra and unrelated signal, which requires correction. This paper presents a novel approach which uses more energetic extreme‐UV light as an alternative to the far‐UV. We show the results of this new algorithm and demonstrate that the measurements line up well with those from other instruments and spacecraft. Key Points We present an algorithm concept for remote sensing thermospheric O and N2, novel in its use of EUV airglow measurements Comparison to related measurements during conjunctions with ICON FUV, GOLD, and Swarm are favorable Retrieval results from 2020 indicate cooler atmospheres than those predicted by MSIS