Answer:
No
Step-by-step explanation:
No, it is impossible to calculate the two masses.
From the statement, there is one known mass on one of the side of the pivot and one "mystery" mass object on the other side of the pivot, so that we have to move that mystery mass or that known mass in a way that it balances both.
We need to know at least one mass. We cannot use any equilibrium condition involving torque with unknown masses.