You got it in one! An inverting buffer (gain = -1), but it must be able to operate correctly with a 0V input which means it has to operate from a - and a + power supply. The + PSU must be greater then say 10.5V, because op-amps again can't handle signals very close to their + rail, So an amp running of +-12V should fit the bill. As this stands this will invert your signal but will result in 10 in, -10 out and 0 in and 0 out. So you have to add a +10V bias to the + input of the amplifier, which should add in the 10V that is missing
Frank