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.
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.
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.
He has no pen to write with
You asked him to write something down, but he can't because he has no pen.
He has no pen which he can write with
You asked him something that is one step removed from "write something down", but where "write something down" was a logical conclusion, such as "take notes" or "make sure you note this".
It's very likely write with is redundant anyway unless the context is such that he might draw or do something else with the pen. Because of this there isn't much difference and the 2nd sentence might be chosen for emphasis or to ensure it is heard/read/understood (wordier sentences have more of a chance of grabbing attention).
The first sentence ends with the preposition "with" so this usage is casual and acceptable in conversation. The second sentence is wrong. To make this formal, the ending preposition should be removed to say: "He has no pen with which to write"