The 1881 and 1901 census are on line but the latter you will have to pay to see detail. The 1881 shows:-
Name Age Birthplace
Elizabeth Tear 39 Manchester
William 21 ..
Jane 19 ..
Frank 17 ..
John 16 ..
Alice A. 12 ..
Mary E. 9 ..
Joseph 7 ..
James S. 8Mths ..
You now need to find who is William's father for your next step back. I've tried IGI ,Free BMD and Lancashire BMD but could not spot him. An 1871 census look up would be helpful.
The age gap between Joseph and James S. is curious when compared to the sequence for the rest of the children and may indicate a change of partner.
If you have no success at finding Williams father try applying to the registry at:-
The application form is on line and I think he is William Teare from Chorlton Vol 8C page 614.
If you find the name of his father ask again on this board and someone will help you .