Solution:

Let the common tangent be: $$y = mx + c$$ For curve $y^2 = 8x$:
Condition for tangency gives: $$mc = 2 \quad \text{(1)}$$ For curve $xy = -1$:
Condition for tangency gives: $$c^2 = 4m \quad \text{(2)}$$ Substitute $c = \frac{2}{m}$ from (1) into (2): $$\left(\frac{2}{m}\right)^2 = 4m \Rightarrow \frac{4}{m^2} = 4m \Rightarrow m^3 = 1 \Rightarrow m = 1$$ Then, $c = \frac{2}{1} = 2$

Final Answer:
$$\boxed{y = x + 2}$$