So, you have a given set $X$, and a specific subset $A$. You know the cardinality/size of $A$, and want to know the cardinality of $X\setminus A$, the (relative) complement of $A$ in $X$. Use $|X|$ to denote the size/cardinality of the set. I will assume the Axiom of Choice so that all sets have comparable cardinalities.
In two cases, this is completely determined by the cardinalities of $A$ and of $X$. They are:
If $X$ is finite, of size $n$; then $A$ is finite, and the size of $X\setminus A$ is $|X|-|A|$.
If $X$ is infinite, and the cardinality of $A$ is strictly smaller than the cardinality of $X$, then the cardinality of $X\setminus A$ equals the cardinality of $X$.
- Reason: If $\kappa$ and $\lambda$ are cardinals, and at least one of them is infinite, then $\kappa+\lambda = \kappa\lambda = \max\{\kappa,\lambda\}$. Here, $\kappa+\lambda$ is the cardinality of the disjoint union of a set of cardinality $\kappa$ and a set of cardinality $\lambda$; $\kappa\lambda$ is the cardinality of the set $X\times Y$, where $|X|=\kappa$ and $|Y|=\lambda$.
For example, $|\mathbb{R}\setminus\mathbb{Q}|=|\mathbb{R}|$, because $|\mathbb{Q}|=\aleph_0 \lt 2^{\aleph_0}=|\mathbb{R}|$. If $A$ is a finite subset of $|\mathbb{N}|$, then $|\mathbb{N}\setminus A|=\aleph_0 = |\mathbb{N}|$.
Unfortunately, this is all you can say. If $X$ is infinite and $|A|=|X|$, then the cardinality of the complement $X\setminus A$ could be anything from $0$ and up to $|X|$. To get a set of size $n$ with $n$ finite, pick any subset $B$ of $|X|$ of size $n$, and take $A=X\setminus B$. To get a set with complement of cardinality $\kappa$ for any $\kappa\lt|X|$, biject $X$ with the cardinal $|X|$, which has a subset of cardinality $\kappa$; take the complement. To get a set of cardinality $|X|$, use the fact that $|X|=|X\times X|$. Then, if $x\in X$ is a particular element, then the subset that corresponds under a given bijection to $X\times\{x\}$ has complement of size $|X|$. For specific sets $X$ it is possible to find specific examples. For $\mathbb{N}$, the even numbers have complement of size $|\mathbb{N}|$. In the real numbers, the unit interval has complement of size $|\mathbb{R}|$. And so on.