It's difficult to sound sincere in a form letter. A letter of explanation is a written, signed and dated document you prepare to address questions a mortgage lender may have about your loan application.It's best to keep your letter of explanation short and sweet. Include as much detail as needed, but address only the specific information the lender requested. A letter of explanation consists of short descriptions you can use to fill in the gaps in your paperwork for your underwriter. Selected income statement data.