Hello Paul,
Elm Tree Hill can be located on a modern map as the junction of City Road, Mansfield Road and Hurlfield Road.
On the maps at
http://www.old-maps.co.uk/ (where the grid reference is 438300 384900) Elm Tree Hill can be seen as a few houses and a pub which must have been dominated by the works and heaps of Woodthorpe Colliery. Just down the road to the east was the village of Intake which also would have housed many miners. Today this is all part of Sheffield's urban sprawl.
I'm guessing that John DURHAM was a miner. I found these two baptisms at
http://www.sheffieldindexers.com:
Durham, George (of Sheffield, born 1839-10-03).
Baptised October 20, 1839, by E Goodwin at Sheffield Parish Church, Church Street, Sheffield.
Parents name(s) are Hannah & John (Miner).
Durham, Henry (of Sheffield, born 1841-10-08).
Baptised November 7, 1841, by T Sutton at Sheffield Parish Church, Church Street, Sheffield.
Parents name(s) are Hannah & John (Collier).
Hugh