Since you want to assume no heat energy is lost from the system, make the two equal to each other in the equation q=mct.
M being mass
C being specific heat
T being change in temperature
(60g)*(c)*(80C) = (10g)*(4.18J/C*g)(2C)
80 is the change in temperature of the solid 100-80= 20
2 is the change in temperature of the water 20-18=2
4.18 is the specific heat of water and you should memorize it because it’s expected of you
So now solve for c:
(4,800g*C)c = 83.6J
c = 0.0174 J/g*C