There is a record at Ancestry which shows Thomas, his wife Magdalene Carlen, and their children. William is not listed. That record is from a compilation made in 1930 and doesn't indicate the source(s) from which the material was drawn. It is a clue at best but here's the citation.
Eshelman, John E., compiler, 1930, "A Genealogical Record of Members Composing The Society of Friends or Quakers Resident at some time in Berks County, Pennsylvania or Attached to the Meeting Located in the said County," pg 72, "Thomas Ellis"; Ancestry.com, database with images, "U.S., Quaker Meeting Records, 1681-1935" > Pennsylvania > Berks > Exeter Monthly Meeting > Genealogy of Berks > image 36 of 206 {{Ancestry Record|2189|2646976}} with attached {{Ancestry image|2189|31906_283788-00480}}. [This record was compiled in 1930; specific sources of the data are not mentioned.]
I didn't find any Quaker records for a William Ellis born in 1814 with a father named Thomas. It was, by no means, an exhaustive search.