Clarence E. Trent was born on September 26, 1904. A native of Northfolk, West Virginia, Trent attended Bluefield Junior College in Bluefield, Virginia, where he earned a two-year academic diploma in 1925. In 1930 and 1931 he earned a BS and an MS in Electrical Engineering at Virginia Polytechnic Institute (now Virginia Polytechnic Institute and State University). In 1935 and 1936 he earned BS and MME degrees in Mechanical Engineering at VPI. Trent was appointed an assistant professor at VPI in 1931, teaching at first in the Department of Mathematics. In 1932 he was sent to Bluefield to organize the VPI Engineering Branch School in cooperation with Bluefield College. He served as head of the Branch School for eleven years. He returned to VPI campus in 1943, where he remained until his retirement in 1973, teaching both electrical and mechanical engineering.

Trent played an active role in the history of the Virginia Section of the Amercian Society of Mechanical Engineers (ASME) from 1945 until his death in 1991. In 1981 he was awarded the grade of Life Fellow of the ASME. Serving on the History and Heritage Committee, Trent was a prime force in the selection of two national mechanical engineering landmarks: the Jackson Ferry Shot Tower at Fort Chiswell, Virginia, and Norfolk and Western Railway's 611 steam locomotive. Trent was the co-author (along with Earl B. Norris) of the book Applied Thermodynamics (New York: McGraw Hill, 1955).

Trent died on December 1, 1991, at the age of 87.