An LM324 will go to 1.25 volts of either rail. If you require the posted schematic to go from 0 to 10V, try an LMC662 (Dual package) It has R/R Input (+/- .3V of supply rails) and Output. There is an LMC6684AIM which is a 12V part that has guarantee'd specs @ 10V. It "can" be accomplished with a '324 but it will require a +15 -5V supply to get the 0 and 10 v limits with a little margin.
Bob