This face has sweat dripping from its brow, due to a stressful situation.
Not to be confused with the Crying Face emoji, which has a tear on the cheek, instead of a bead of sweat. At small sizes the difference can be difficult to discern.
Grammatically, this may have been better named Disappointed Yet Relieved Face.
Sad but Relieved Face was approved as part of Unicode 6.0 in 2010 under the name “Disappointed but Relieved Face” and added to Emoji 1.0 in 2015.
😥 Eyebrow Sweat
😥 Disappointed but Relieved Face