Do plugin

x = y^2-2

x^2 = (y^2-2)(y^2-2) = y^4-4y^2+4. So y^4-4y^2+4=y+2. Then y = y^4-4y^2+2. Begin to test values starting with 5 and getting smaller. For 5, it doesn't work. It is very far, so we try 3. For 3, we have 81 = 36+2 which is false. For 2, we have 2 = 16-16+2 which is true so y = 2 and x = 2 clearly.