How to convert isometric coordinates to cartesian coordinates with scale factor and offset

Question

I use this algorithm to convert cartesian to isometric

    // convert cartesian to isometric
    sx = ((x - y) * (tile_width / 2)) * scale_width + offset_x;
    sy = ((x + y) * (tile_height / 2)) * scale_height + offset_y;

Considering this algorithm, how do I get the map coordinates?