Assume there is a common secret $x$ that is used to conceal the value of $a$ and $b$, known only by the actors possessing $a$ and $b$. A verifier $c$ is a randomly picked number, and provided to the two parties possessing $a$ and $b$. Then, they calculate $ax-c$ and $bx-c$, and provide them to the verifier. The verifier then calculate the difference between $ax-c$ and $bx-c$, which is the result. In such case, because $ax-c$ and $bx-c$ is not definitely divisible by $x$, there are no ways of the verifier figuring $x$ out.
Note that there are problems with this protocol, as it requires interaction between the verifier and the two parties bearing $a$ and $b$.
EDIT: The actual possibility of the provers A and B counterfeiting their values
There are two cases of the identity of the verifier, which should be discussed separately. The first possibility, is that the verifier is the auctioneer. In this case, A and B would always attempt to counterfeit their value, since the auctioneer has no way of knowing the value of $x$. They would both do the same thing, not using their mutually known $x$, but something else. In such a case, their actions cancel each other out. However, if the verifier is a spectator, there are no reasons for them to counterfeit a value, and even if they do so, the spectator would always know. Therefore, the problem of counterfeiting a value is actually not existent.