Quadratic Equations

let the two numbers be x and y
so x-y = 2... equation 1 according to the first condition

also, smaller number being added to square of larger number is -12 as you have written it, it is not possible, since you are adding a smaller number to the square of a larger number (positive number),
if it is 12, the sum

then second equation can be framed as
y+x^2 = 12
eliminate y from both equations
y=x-2 from equation 1

y = x^2 - 12 from second equation
equating
x-2 = x^2 -12
this is a quadratic, solve it for your values of x, and substitute for values of y
http://www.wolframalpha.com/input/?i=x-y%3D2%2Cy%2Bx%5E2%3D12
here is your values of x and y

Sorry for the typo, it supposed to be "one" not "on".

a - b = 2

a is bigger
b is smaller.

b + a^2 = -12

now you have to solve for a and b

b = -12 - a^2

so

a - -12 - a^2 = 2

-a^2 + a + 12 - 2 = 0

-a^2 + a + 10 = 0

Use quadratic formula

the roots should be

3.701562119 and -2.701562119

weird