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 one-hundred-twenty 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 a dozen other states. He is also registered with the International Registry of Professional Engineers.

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 aquatic facilities in the hospitality and entertainment industries worldwide.

In 1977, Terry and Tom Barber formed Barber-Brannon, Engineers, a  partnership which would eventually become The Brannon Corporation. From 1985 to 2000, Terry was the chief executive officer and president of the company. No longer burdened with being the CEO, he is now Chairman Emeritus but still holds the office of President.

Besides the company he founded, Terry also sits on the board of directors for two international corporations.

He enjoys snow skiing in Colorado and traveling with his wife. He is a deacon, choir member and teacher at Green Acres Baptist Church.