I think that this sentence is mostly correct however I think it is more natural to say that “10 days HAVE gone BY since your last letter.” The difference between had and have is just about the tense if you were trying to speak in the past tense then yes had would be correct but for the present tense have is better. Also your use of the word since good but it is much more natural to say 10 days have gone by than 10 days have gone because the use of the word by is just showing that the time has passed. Hope this helps!