You can use the INDIRECT function for this, for example
=SUM(INDIRECT(B2):INDIRECT(C2))
if you can live by entering the entire cell name (A10, A25).
Or just have numbers in B2 and C2, you can use
=SUM(INDIRECT(ADDRESS(B2;1)):INDIRECT(ADDRESS(C2;1)))
(Hope I got the columns and rows in the correct order!)