I agree that the chance of getting all those letters in that order from any given starting point is 1/28^18 
I agree with how many letters are typed in a year. 
But after that you lost me. 
There is probably some key thing that I am supposed to understand but I do not understand.
In reality, the monkey could get that combination on the first go - it is afterall just as likely as any other set of 18 characters.
OR
The monkey could type away for any finite period and the sentence will not appear.
I am sure that someone could work out the probability of it a appearing in any given period of time but I do no see how they could specify exactly how long it would take.
Like I said, I expect I am missing some key understanding of what is being asked here. 