I'd forgotten I had contributed a little to the other thread.
Jim1 is absolutely correct (he always is) with the sequence of battalions. However, what none of us can say is when he transferred from one battalion to another. The only sure dates are:
He went to France after the start of 1916 (his medals do not include the 1914 or 1914-1915 Star which means no overseas service before end 1915).
He can only have been in 3/10th between 1 Jun 1917 and 20 Feb 1918 (its dates in France) although he may have stayed on in 11th Entrenching Battalion for an indeterminate time if he was there at the end before being posted to the 4th Battalion (a draft of 47 men from somewhere joined the 4th on 24 March - could he have been one of them, perfectly possible).
jim1 has already looked at war diaries to see if there are entries in the 18th that show men going to 3/10th and found no evidence. He has also looked at the 4th and has found men arriving on Feb 12th 1918. I would venture to suggest these were not from 3/10th who themselves received a draft of 300 men on 8 February from 11 Battalion which was broken up in that month, they are more likely to have been from 11th also.
The situation really is that, without his service record, one can only say that your ggrandfather served in the 3 battalions in the order jim1 found for you in the medal roll but with no idea when (apart from not being able to be in 3/10th before 1 Jun 1917 or after 20 Feb 1918).
If you felt like cross checking yourself, each diary is downloadable for £3.50 from the National Archives or you can see them on Ancestry if you get the sub we've been recommending. Be aware though, as jim1 has said already, individual soldiers are rarely named in war diaries, the best to be hoped for would be an entry that say "x men to 3/10th" or "x men from 3/10th" but even then was he one of them - who knows?
MaxD
http://discovery.nationalarchives.gov.uk/details/r/C7353815 - 18th battalion
http://discovery.nationalarchives.gov.uk/details/r/C7352155 - 3/10th
http://discovery.nationalarchives.gov.uk/details/r/C7354085 - 4th