Yes, there is a user-replaceable date/time battery in the SX10 IS camera.
It's in a little "drawer/holder" off to the side in the main battery compartment. First remove all of the AA batteries. Then you can slide out that little drawer/holder. You'll need a fresh CR1220 lithium battery. Watch the orientation is correct, then slide back in. I also like to wipe with something lightly dampened with isopropyl alcohol, so that any finger oils are off the battery.
This time/date battery change process is illustrated on page 265 of the user manual.
If you don't have your manual, it's available to download as a PDF here: https://www.usa.canon.com/support/p/powershot-sx10-is
This is a rather common setup on older Canon cameras. Some have the battery drawer/holder located elsewhere (Eg... EOS 5D and 5DII have it under all the connectivity sockets).
Newer cameras have a permanently installed, rechargeable battery right on the motherboard. It gets recharged from the main user-rechargeable battery(ies).
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7DII (x2), 7D(x2), EOS M5, some other cameras, various lenses & accessories
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