f[x_, y_] = 
        x^2 + y^2 + (x^2 + y^2)^2 - 1;
g[x_, y_] = x + y + x^2 + y^2 - 1;
Plot3D[
      f[x, y], {x, -1, 1}, {y, -1, 1}]
Plot3D[g[x, y], {x, -1, 1}, {y, -1, 1}]

Plot3D[f[x, y] - g[x, y], {x, -1, 1}, {y, -1, 1}]