If you are interested in a simpler calculation that gives an approximation of dew point temperature if you know the observed temperature and relative humidity, the following formula was proposed in a 2005 article by Mark G. Lawrence in the Bulletin of the American Meteorological Society:
Td = T - ((100 - RH)/5.)
where Td is dew point temperature (in degrees Celsius), T is observed temperature (in degrees Celsius), and RH is relative humidity (in percent). Apparently this relationship is fairly accurate for relative humidity values above 50%.
More details can be found in the article:
Lawrence, Mark G., 2005: The relationship between relative humidity and the dewpoint temperature in moist air: A simple conversion and applications. Bull. Amer. Meteor. Soc., 86, 225-233. doi: http;//dx.doi.org/10.1175/BAMS-86-2-225