How can I do minus on plaintexts in the Paillier cryptosystem? We have $E(a)$, $E(b)$ encrypted under the same Paillier key.

As we all know, we can get $E(a+b)$ by calculating $E(a)*E(b)$.

But can we get $E(a-b)$, by calculating $E(a)/E(b)$?

I tried to calculate $E(a)/E(b)$ by using the mpz_divexact function in the GMP library. But I cannot get the correct result.
In Paillier, as you note, multiplication in the ciphertext domain translates to addition in the plaintext domain. Thanks to the algebraic structure behind Paillier what you can do to get subtraction is use the multiplicative. This works fine when the result is positive. When the result is negative, however, you would like to return that value, but what decryption will return is something between $0$ and $n-1$. For example, if the result is $-1$, you will see $n-1$. To deal with this, we can set some threshold (will depend on the application). If the decrypted value is greater than that threshold, return that value minus $n$. For example, if we see $n-1$ on decryption, we will return $n-1-n=-1$.