Elisha was the son of Capt. Solomon Holman and Mercy (Waters) Holman. He was born May 13, 1739.
"Massachusetts, Town Clerk, Vital and Town Records, 1626-2001," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:F4FR-DM6 : 10 November 2020), Elisha Holman, 13 May 1739; citing Birth, Sutton, Worcester, Massachusetts Bay Colony, British Colonial America, Massachusetts Secretary of the Commonwealth, Boston; FHL microfilm 007009440.
Therefore, he is the full brother of Jonathan Holman.