10 Commonwealth Avenue was built for Thomas Appleton in 1864 and demolished in 1963 perhaps to make way for an addition to the Ritz Carlton Hotel, which was completed in 1981. Given the delay between demolition and construction there is some question as to why the addition took so long to be approved and if two events are in fact related.
Appleton is an important figure in 19th Century Boston, known for his art collecting and work for the Boston Public Library. According to Bainbridge Bunting, 8 and 10 Commonwealth Avenue were built by friends (Erastus Bigelow occupied number 8). Bunting states that the while number 8 was two feet wider than number 10, number 10 had a second floor library which extended across the south side (rear) of both houses. For more information on the architecture of the Back Bay, I recommend Bainbridge Bunting's Houses of Boston's Back Bay: An Architectural History, 1840-1917. You can read more about the addition to the Ritz Carlton at Architectural Boston's thread on the Ritz Carlton.