Martin Gardner's research, now largely discredited, proposes that the real Erdnase was Milton Franklin Andrews, and that the book was ghost-written by William John Hilliar. (S. W. Erdnase spelled backwards is E.S. Andrews, lending support to the theory that Andrews was the author's last name)
There are numerous possible candidates discovered by David Alexander, Richard Hatch, and Todd Karr (among others), any of whom might be the pseudonymous author. The candidates by Alexander and Hatch have been profiled in (respectively) Genii, MAGIC and Magicol. Karr's candidate is identified as a Midwestern-based con artist named E. S. Andrews who was active around the turn of the century and whose biography seems to fit Erdnase's.