Can you find the mass of solvent with mass of solute, volume of solution, and solution density?
That works!  In most chemistry (but not nuclear reactions!),  mass is always conserved, so 

$$m_\text{solution} = m_\text{solvent} + m_\text{solutes}$$

Mass is also equal to density times volume, so

$$m_\text{solution} = \rho_\text{solution} V_\text{solution} = m_\text{solvent} + m_\text{solutes}$$

Solving for $m_\text{solvent}$:

$$m_\text{solvent} = \rho_\text{solution} V_\text{solution} - m_\text{solutes}$$

Which is exactly the calculation you did.