= Solution
At a molecular line, the large opacity moves the optical-depth-one surface to lower pressure and higher altitude than the neighboring continuum. The <Eddington-Barbier relation> makes the emergent intensity approximately the <Planck function> at that layer. In an ordinary outward-cooling atmosphere, the line-forming layer is cooler and the feature is in absorption. In an <atmospheric thermal inversion>, it is hotter, so the <spectral-line emission from an atmospheric thermal inversion> exceeds the continuum brightness and the feature appears in emission.
Factors that can create or suppress inversions include the abundance of high-altitude optical absorbers such as TiO, VO, or atomic metals; the host star's irradiation level and spectral energy distribution; and clouds, hazes, composition, and day-night circulation, all of which alter where stellar and thermal radiation are absorbed.
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