What's the general mathematical method to go about solving a substitution cipher? Here's a question from a professor's page:

Decipher the following simple-substitution cryptogram, in which every
  letter of the message is represented by a number. 

8 23 9 26 4 16 24 26 25    8 18    22 24 13 22 7 13 22 8    8 18 19 7

Hint: The most frequent letters in English in descending order are:
  ETAOINSHRDLU

I solved it by brute force, just guessing letters, 

 "this sentence is backwards", written backwards

but I'm curious to know if there's a mathematical way to go about solving it on paper? 

This is a trick question.  Following the hint, we should first look for solutions involving ETAOINSHRDLU, and in fact the solution has three E's, a T, two A's, etc., so we will find it this way much faster than guessing randomly.  But will we know it when we see it?  If we are validating a solution by checking if it is an English sentence, as the hint suggests we do, we will fail to identify it, since it is written backwards.  It is hard to imagine a general method that would be able to solve this as a special case; would it have to know that "sdrawkcab" is "backwards" written backwards?  What if instead the cryptogram was "the letters of this sentence written in sorted order" with the letters written in sorted order, i.e. "cddeeeeeeeeef..."?  If the answer were actually an English sentence the hint would be useful.  But it is also such a short string that I would be surprised if there are not many other grammatically-correct assignments.
