Since 1969, Terry has worked in public works for cities and counties.  Beginning with the City of Irving, Texas and ending eight years later with the City of Tyler, Texas,  Terry's early career was spent working in the engineering departments of these two cities. Since 1977, his work designing water systems, sewer systems, parks and recreation facilities, airports, public buildings, drainage and paving has expanded to more than eighty different local governments.

Terry graduated from the University of Texas at Arlington with a baccalaureate degree in Civil Engineering in 1973 and received his license to practice engineering in Texas in 1976.  Later he would add licenses to practice in Louisiana, Mississippi, New Mexico, Oklahoma, and Georgia. He is also licensed to practice in Nebraska.

Specializing in water conveyance and treatment, Terry's experience has been broad based ranging from design of water and wastewater treatment plants, to performing stormwater and floodplain studies, to design of competition swimming pools and aquatic centers.

In 1977, Terry and Tom Barber formed Barber-Brannon, Engineers, a  partnership which would eventually become The Brannon Corporation.  Since 1985, Terry has been the chief executive officer and president of the company.

Terry's outside interests include singing Southern gospel music in a quartet at his church.  He enjoys snow skiing in Colorado and traveling with his wife.  He is a deacon, choir member and teacher at Green Acres Baptist Church.