grammatically speaking...

[Lois Nathan]

Joanne,
    I'm trying to identify what is different between your three examples
"send me an e-mail, drop me a line, write me when you get back" which work,
and "explain me what you mean," which I don't think works.

It may be usage or the functioning of the verbs themselves.  In your three
examples there's very little ambiguity in putting the indirect object before
the direct object.  The "me" in "send me" and "drop me" as dierct object
would be very little used, except for example in the song: "Yoooou send me."
"Drop me" would suppose "you" were holding "me".  But I think one "explains"
something to someone, in that order.  To "explain someone" could exist.  "I
can explain him" for example.  That would be to explain that person so that
others could understand him, if he were impenetrable.
In contrast, "tell me something" or "tell something to me" both work in that
form.  But "tell me" isn't ambiguous.
Just food for thought.

Lois Nathan