It seems you might be mixing up the story with the TV series. In the TV series, Eb (played by Michael Landon Jr.) lives with the Ingalls family for a time. However, in the book "Little House on the Prairie," Eb is not a character at all.
The "Little House" books by Laura Ingalls Wilder are based on her own life and do not include a character named Eb. It's likely you're thinking of the TV series which took liberties with the original source material.