Glossbrenner was born in Hagerstown, Maryland. He learned the art of printing, and became publisher of the Western Telegraph in Hamilton, Ohio, in 1827 and 1828. He moved to York, Pennsylvania, in 1829. He established the York County Farmer in 1831, and became a partner in the York Gazette in 1835, and continued his connection with that paper until 1860.
Glossbrenner was elected as a Democrat to the Thirty-ninth and Fortieth Congresses. He was an unsuccessful candidate for reelection in 1868.
Following his political career he engaged in banking in York in 1872. He moved to Philadelphia in 1880, and was employed by the Pennsylvania Railroad until his death in Philadelphia in 1889, aged 78. He was interred in Prospect Hill Cemetery in York, Pennsylvania.