Which sentence is correct?
My teacher is too tired to explain that topic.
My teacher is too tired explaining that topic.
Too tired to explain
means that he is so weary that he cannot explain—perhaps he cannot concentrate think clearly.
tired explaining is not a fixed construction, but tired of explaining is:
Too tired of explaining
means that he he has explained so often that he has become annoyed—he refuses to explain any more.
"too tired to explain" is right.
Strange though it may be, the only way I can explain this is by comparing it with a phrase in German:
"zu müde um zu erklären"
It means for the purpose of explaining; hence the "um" in German, and hence the "to" form rather than the "-ing" form must be used.