The complete sentences are:
"He has no pen to write with."
and:
"He has no pen which he can write with."
The book does not explain the differences in meaning between these two. So, please tell me about the differences.
Learn English – “no pen to write with” vs. “no pen which he can write with”
grammar
Best Answer
You're going to get a lot of people telling you not to end sentences with prepositions. You can generally ignore those suggestions. Source, source, source, source, source, etc. ad nauseam. That said, the second sentence does sound more natural with the preposition shifted. The reason is simply that the preposition's object (the pronoun which) is already present, so it is typical to place the preposition in front of that: "He has no pen with which he can write." In the first sentence, the object of the preposition is implied, and to shift the preposition you would have to add it. You don't need to do that, on the basis of an artificially curmudgeonly, non-existent rule.
Regarding your actual question: Either sentence is correct, and there is very little difference in meaning between them. There's a slight difference in register—the second sentence sounds a bit more formal, especially if you do shift the preposition.