Sometimes in the census records it will "adopted son" instead of just son. The records I found do not show that. He did have a sister Freelove that was older than him. What might help is if you know the church they belonged to in Hammond and go to the church and look up both Freelove's and Earl's baptism record. It may mention in there if he was. That is about the only record at this time that might be available since in was in 1880. I have done a lot of research over the years and church records have been very helpful!
Addison and Mary Jane Gogin (how record is showing) married in Pierce County, WI Jan 1, 1876.
Best of luck.
Faith