1) The three examinees don't know each other (so initially don't know anything about the other's predilection to tell truth or lie).
2) The three also don't know that the glasses only help the correct owner to see properly (so have no idea how well the others can see).
3) A's statement should be read as "I clearly perceive that the first letter is an E!" - i.e. A claims both that they can see the letter and that it is an E. This is to avoid a situation such as a joker mistakenly believing they can see an E (when it is really an F for example), and attempting to tell the truth.
4) The truth tellers and liars are 'classical' in the sense that:
- if T knows X=Y, then T can say X=Y
- if L knows X=Y, then L can say X<>Y
- if J knows X=Y, then J can say X=Y or X<>Y
- if T,L,or J doesn't know if X=Y, then T,L, and J cannot say either X=Y or X<>Y
I think the solution hinges on B's statement.
"A is lying!" can only be said by someone who can see properly. If B can see, then their statement is conceivably true: For example B sees that the letter is not an E, so knows A must be lying. Alternately, B's statement can be conceivably false: For example B sees that the letter is an E (assumes A is telling the truth) and lies about it. If B couldn't see then B can't be trying to tell the truth (how would B know if A lied?), and B can't be attempting to lie (because for all B knows, A could already be lying so B would inadvertently tell the truth).
So now all we need is to do is confirm if there is at least one ordering of truth teller, liar, and joker that would be consistent with the statements made. (Note that as we don't know if the letter is an E or not, we have to find a solution that is consistent in either case).
If the first letter is an E:
LJT is a consistent ordering. A doesn't know what the letter is and lies that he/she perceives an E (accidentally getting it correct). B, who can see that it is an E, mistakenly believes A has made a true statement and lies about it. C, who cant see, truthfully admits the fact. So the examiner confirms B owns the glasses.
If the first letter is not an E:
LTJ is a consistent solution. A doesn't know what the letter is and lies that he/she perceives an E (accidentally getting it wrong). B sees that the letter is not an E and tells the truth about A. C decides to be honest and admits he/she can't see. So, once again, the examiner confirms B owns the glasses.
So in either case, the examiner can confirm B owns the glasses and can fail all the examinees for cheating.