Can anybody decipher the date? Model # 110.87181180
Your dryer is probably a 1981 model.
For most vintage Kenmores, the model year was decoded by the first two digits after the 110. If I am correct, by the 1980s the first and third digits after the 110 decoded the model year.
If I infer correctly your dryer is one of the black paneled center dial models. They were manufactured from 1976 to 1985, possibly 86. 1986 was when the direct drives took over the inventory at Sears, and the dial was moved back to the right end of the panel. So your dryer would more likely be a 1981 model.
Have a good one,
James