How did Sherlock Holmes know the person visiting him was a teacher?

In "The Red-Headed League," the person visiting Sherlock Holmes isn't a teacher—he's a writer.

The plot centers around Jabez Wilson, a former laborer who is now the owner of a pawn shop of middling success. Wilson is approached by his assistant, Spaulding, about a lucrative opportunity for work presented by the so-called "Red-Headed League." Having red hair himself, he inquires about the work. The job is busywork that pays far beyond the actual skill required...

In "The Red-Headed League," the person visiting Sherlock Holmes isn't a teacher—he's a writer.

The plot centers around Jabez Wilson, a former laborer who is now the owner of a pawn shop of middling success. Wilson is approached by his assistant, Spaulding, about a lucrative opportunity for work presented by the so-called "Red-Headed League." Having red hair himself, he inquires about the work. The job is busywork that pays far beyond the actual skill required to do it, specifically, four pounds per week to hand-write a copy of the Encyclopedia Britannica. 

When Wilson arrives at Holmes's Baker Street abode, Holmes makes a number of deductions on sight—Wilson's history as a laborer, his travel to China, and, of course, his role as a writer. Holmes makes this deduction from Wilson's sleeves—the right hand, Wilson's writing hand, is "shiny" in the cuff of his shirt, and the left elbow has a worn spot from where Wilson rested it on his desk.