R=R₀(1+α(T-T₀)), where R₀ is the resistance at T₀=20°C, T is the temperature for which we want to calculate the resistance and α is the temperature coefficient for resistance.
The resistance of the copper wire increases by 18% or by 0.18, so the new value for the resistance is R=1.18*R₀.
Now we need to input that into the equation for resistance change and solve for temperature T.
1.18R₀=R₀(1+α(T-20)), R₀ cancels out,
1.18-1=α(T-20), we divide by α,
0.18/α=T-20, we put 20 on the left side,
So the temperature on which the resistance of copper wire will increase by 18% is T=46.47°C.