Let x be the first number and y be the second number.
From the problem statement, we know that:
The sum of the two numbers is zero, so x + y = 0.
One number is eleven less than the other, which means x = y - 11.
We can substitute the second equation into the first equation and get:
y - 11 + y = 0
Solving for y, we get:
2y - 11 = 0
2y = 11
y = 11/2
So the second number is 11/2 or 5.5, and the first number is eleven less than the second number, which is -5.5.
Therefore, the two numbers whose sum is zero and one number is eleven less than the other are -5.5 and 5.5, respectively.