Tenga, son of Ingvar, was an (apparently) human spellcaster and a reclusive hermit that lived in Edur Ithindra which was an ancient, abandoned elven outpost. Eragon (at the time separated from Saphira) came into contact with him in the third novel, Brisingr, after his successful defeat of the Ra'zac, the subsequent flight from Helgrind, and the banishment of Sloan for his crimes.
Initially appearing to be little more than slightly eccentric, Eragon was shocked to discover Tenga's vast array of Compendiums of the Ancient Language. Perhaps more startling was Eragon's observation that Tenga used magic silently, a practice thoroughly discouraged, even by the elves. These questions pose the possibility of him being a Grey folk descendant.
Tenga informed Eragon that he was in search for the answer to "the question," though he failed to detail what that question might be. There was foreshadowing that implied that the question could have a significant impact on the crisis with Galbatorix, though the reader was never informed as to how. Frightened by the man's vehemence towards the topic (as well as his apparent insanity), Eragon slipped away during Tenga's rant, though he appeared to be oblivious to Eragon's departure. However, Tenga knew Eragon was there when he was somewhat concealed upon arriving at Edur Ithindra. Tenga also had the power of observation to know that a similar question burned in Eragon's heart. There seemed to be more to Tenga than he wants others to believe.
Eragon recounted his adventures upon his return to the Varden, and was startled by Angela's revelation that she was Tenga's apprentice for a time. She informed Eragon that Tenga was "constantly searching" for an answer to "the question", and implied that the scope of said questions varied from trivial in nature to profound. She also noted that after solving the question currently occupying him, Tenga would "invent" a new one. His "questions" mostly related to divining the secrets of elemental forces. Solembum added that he is 'a man who kicks at cats.'
As part of Nasuada's plan to keep watch over magic users, she sent four spellcasters to Tenga's watchtower. When they did not return, she asked Arya and Fírnen to investigate. They discovered the bodies of the spellcasters but found no trace of Tenga.
In an interview, author Christopher Paolini stated that "Tenga was searching for something much more important than whether the rocks in the Beor Mountains are affected by the stages of the moon." Given this statement and Galbatorix's 40 year search for the Name of Names, it is possible that Tenga was searching for the Name of Names as well. It is also possible, due to what he says about a "key to an unopened door", that Tenga was searching for a way to use the energy from fire and light.