Or HaChaim on Numbers 12:9/אור החיים על במדבר י״ב:ט׳

1 ויחר אף השם, G'd's anger was kindled, etc. He was irritated at them and snorted at them, i.e. a description of a nasal reaction. וילך, "He went;" G'd went away in order to give vent to His irritation. Although we find a different formulation in Exodus 4,14 where the Torah reports ויחר אף ה׳ במשה, "G'd's anger was kindled at Moses," followed by a verbal retort from G'd, the situation was different then. At that time G'd wanted to activate His anger against Moses by depriving him of a spiritual power, i.e. the fitness to become the High Priest; He gave that distinction to Aaron instead as pointed out in Zevachim 102. The Talmud discusses whether mention of G'd becoming angry necessarily has an immediate noticeable consequence. In our instance, G'd imposed a severe penalty as a person afflicted with Tzoraat is considered as no better than dead (verse 11). The Torah writes בם, that G'd was angry at both Miriam and Aaron, to tell us that both were afflicted with Tzoraat. The difference was only that Aaron was cured immediately, whereas Miriam was not cured immediately, so that no one but Miriam and Moses had been aware that Aaron too had been afflicted with Tzoraat if ever so briefly.