A United States president who served before Richard Nixon whose last name starts with an E would be Dwight D. Eisenhower. There was never a president (before or after Nixon) to have a first name that starts with the letter E.
Richard Nixon's Vice President, Gerald R. Ford, assumed the presidency when Nixon resigned in 1974. Ford served the remainder of Nixon's second term and ran in the 1976 election. However, he was defeated by James E. (Jimmy) Carter.