Given that n(P U Q) = n(P U Q)', find x and hence find n(8).

The number of elements in $P \cup Q$ is the sum of elements in $P$ only, $Q$ only, and $P \cap Q$.

$$n(P \cup Q) = (x - 16) + 4 + (x - 11)$$ $$n(P \cup Q) = x - 16 + 4 + x - 11$$ $$n(P \cup Q) = 2x - 23$$

From the Venn diagram, $n(P \cup Q)' = x$.
Substitute the expressions into the given condition:

$$2x - 23 = x$$

Subtract $x$ from both sides:

$$2x - x - 23 = 0$$ $$x - 23 = 0$$

Add 23 to both sides:

$$x = 23$$

So, the value of $x$ is $\boxed{\text{23}}$.

The total number of elements in the universal set, $n(\mathcal{E})$, is the sum of elements in $P \cup Q$ and elements outside $P \cup Q$.

$$n(\mathcal{E}) = n(P \cup Q) + n(P \cup Q)'$$

Since we found $n(P \cup Q) = 2x - 23$ and $n(P \cup Q)' = x$, and we know $x=23$:
$n(P \cup Q) = 2(23) - 23 = 46 - 23 = 23$.
$n(P \cup Q)' = 23$.
Therefore,

$$n(\mathcal{E}) = 23 + 23$$ $$n(\mathcal{E}) = 46$$

The value of $n(\mathcal{E})$ is $\boxed{\text{46}}$.