There are quite a few Thomas Dawson's born around 1878/9 in Lancs- none living specifically in Manchester. As Mary suggested you will need to give us more info.
Presumably when you say he was married to E? that would have been after 1901?
One of us will take another look once we know a bit more.What job did he do by the way- or do you know his parents or any brothers or sisters names?
Name Age in 1901 Birthplace Relationship Civil Parish County/Island .
Thomas Dawson 23 Chorley, Lancashire, England Boarder Bolton Lancashire
Thomas Dawson 23 Bolton, Lancashire, England Son Bolton Lancashire
Thomas Dawson 21 Bolton, Lancashire, England Son Bolton Lancashire
Thomas Dawson 22 Hampstead, London, England Boarder Crumpsall Lancashire
Thomas Dawson 21 Farnworth, Lancashire, England Son Farnworth Lancashire
Thomas Dawson 21 Gorton Son Gorton Lancashire
Thomas Dawson 23 Horwich, Lancashire, England Son-in-law Horwich Lancashire
Thomas Dawson 23 Oldham, Lancashire, England Head Oldham Lancashire
Thomas E Dawson 21 Sandbach, Cheshire, England Boarder Skelmersdale Lancashire
Thomas Henry Dawson 21 Lancaster, Lancashire, England Son Lancaster Lancashire
Thomas M Dawson 21 Scotland Son Bolton Lancashire
TAKE YOUR PICK

Regards
Carol