Brough's career as an artist began in earnest during World War II while he served in the Special Services of the U.S. Air Force as an artist. After more than four years in Texas and at the European Theatre, an area of heavy fighting across Europe, he graduated from Chouinard's Art Institute in Los Angeles. The Chouinard Art Institute was a leading professional art school founded in Los Angeles in 1921. It was later absorbed into the California Institute of the Arts. After his graduation, Brough trained in San Antonio, Texas, at the Witte Museum/San Antonio Museum of Art, and in Paris, France, at the Académie de la Grande Chaumière. He also worked with motion pictures and television and as a free-lance artist.
Brough began his teaching career as a graphic designer. In 1985, after 37 years of service, he was awarded UA's highest teaching honor, the Outstanding Commitment to Teaching Award. He was nominated for the award by former students, many of whom described him in nomination letters as "the best teacher I've ever had." For 15 years, Brough also commuted to Birmingham, where he taught watercolor classes for the University Center Continuing Education Program.
During Brough's tenure at UA, he combined teaching with a successful career as a commercial artist. He maintained a private studio in Tuscaloosa, Alabama, until his death on December 22, 1996, at 76.