Other forms: epistolarily
Any correspondence, communication, or other text written in the form of a letter or series of letters is said to be epistolary.
They've gone out of fashion now, but in the 18th and 19th centuries, the "epistolary novel" — written in the form of fictional letters to and from various correspondents — was all the rage. One of the most famous such novels is Bram Stoker's Dracula. Along with other things, like newspaper clippings and journal entries, the story is told through telegrams and letters exchanged between characters. Epistolary is related to the word epistle, a fancy term for "letter."