Use of indexes in tensor calculus

Question

I'm reading Carlo Rovelli's "General relativity" and I'm sometimes puzzled about the way he uses indexes (I haven't studied tensors in a formal way, just googled something). For instance, one exercise asked to determine what happens when we change variables in a frame field: suppose we have a surface with some general coordinates $x^a=(x^{1},x^2)$ and we want to move to the coordinates $y^a=(y^1,y^2)$. Then Rovelli claimes that the new frame field is $E_{a}^{j}=\frac{\partial x^b}{\partial y^a}e_b^j$, where $e$ represents the former frame field. I don't understand where does the $b$ index come frome, could someone explain it to me?