Much like @Meiffert I determined that:
Charles was born in 1976.
The equations used are the same but rather than looking at the possibilities I used more maths to eliminate options.
So we start with:
$99 − 10x − y = 1 + 9 + x + y$
$11x + 2y = 89$
And then make the following deductions:
Since $11x+2y$ is odd and $2y$ is always even, $11x$ must be odd. So $x$ is odd.
Similarly since $2y<19$ then $89-11x<19$ so $11x>70$ so $x>6$.
Lastly $11x < 90$ must be true, or $y$ would be negative which doesn't make sense. Thus $x < 9$.
So $x$ is odd. $x$ is less than $9$. $x$ is greater than $6$. This leaves $7$ as the only possible value for $x$ and then we simply work out $y$ is $6$ for the answer.