To reach exactly 0V, you'll need a negative supply, and likely a larger positive supply, and a better opamp then either of those two opamps.
The LM348 says max output is +/-12V when VCC is +/- 15V. So that means it can get to within 3 volts of the power rails. It gets worse as output load goes down.
The LM324 output high voltage can reach Vcc - 1.5V and the output low voltage can reach to within 0.5V of GND.
So you see neither of these can reach the top rail or ground rail on their outputs, so you won't be able to use it to go 0 - 10V. What you need to use is what's called a RRIO OpAmp (Rail-to-Rail on Input-and-Output) . Then the input can go 0 - 5V and the output can reach your required approx. 0 - 10V. RRIO opamps still can't reach all the way down to 0 volts when using a single supply, but some of them can get closer to 0 volts than others.
There are plenty of RRIO opamps. I just went to Digikey, used the parametric search, chose RRIO, Vsupply range min 12V max 60V and, max Vos of 5mV and sorted by price, and I found the
Micrel LMC7101, it can get to within about 300mV of either rail. The
Texas Instrument's TL971 is also a RRIO opamp, has max Vos= 4mV, and can get to within 100mV of each rail. Both chips are about $1.00 for QTY 1. Both of these can operate with a 12V supply.
In this thread:
https://www.eevblog.com/forum/projects/recommended-single-supply-rail-to-rail-jellybean-op-amp/msg448870/#msg448870@poorchava recommends the
LM358 and
LM2904, both of which can swing their output to within 20mV of GND, but can only go to within 1.5V of the upper rail. So if you need 10V out, you need to run the Vsupply at around 12V or more to give enough headroom. If you can get the supply to 12V or more, then you can use these much cheaper opamps, they are about $0.55 and $0.41 respectively.
That thread also recommends OPA192 but it will be expensive at $4 each.