To simplify the expression \((\sqrt{3 - \sqrt{2}})^2 + \sqrt{27 + 10\sqrt{2}}\), we will first simplify each term separately.

1. **Simplifying \((\sqrt{3 - \sqrt{2}})^2\)**:

\[
(\sqrt{3 - \sqrt{2}})^2 = 3 - \sqrt{2}
\]

2. **Simplifying \(\sqrt{27 + 10\sqrt{2}}\)**:

We will attempt to express \(27 + 10\sqrt{2}\) in a simpler form. We assume it can be expressed as \((a + b\sqrt{2})^2\).

Expanding \((a + b\sqrt{2})^2\) gives:
\[
a^2 + 2ab\sqrt{2} + 2b^2
\]
This leads to the equations:
\[
a^2 + 2b^2 = 27
\]
\[
2ab = 10
\]

From \(2ab = 10\), we have:
\[
ab = 5 \quad \text{or} \quad b = \frac{5}{a}
\]

Substituting \(b\) into the first equation:
\[
a^2 + 2\left(\frac{5}{a}\right)^2 = 27
\]
Simplifying, we get:
\[
a^2 + 2\left(\frac{25}{a^2}\right) = 27
\]
Multiplying the entire equation by \(a^2\) to eliminate the fraction gives:
\[
a^4 - 27a^2 + 50 = 0
\]
Letting \(x = a^2\), we have:
\[
x^2 - 27x + 50 = 0
\]
Solving this quadratic equation using the quadratic formula:
\[
x = \frac{27 \pm \sqrt{27^2 - 4 \cdot 50}}{2}
\]
\[
= \frac{27 \pm \sqrt{729 - 200}}{2}
\]
\[
= \frac{27 \pm \sqrt{529}}{2}
\]
\[
= \frac{27 \pm 23}{2}
\]
The two roots are:
\[
x = 25 \quad \text{(corresponding to \(a=5\))} \quad \text{and} \quad x = 2 \quad \text{(corresponding to \(a=\sqrt{2}\))}
\]

Thus, we take \(a=5\) which implies:
\[
b = \frac{5}{5} = 1
\]
Therefore:
\[
\sqrt{27 + 10\sqrt{2}} = 5 + \sqrt{2}
\]

3. **Combining Results**:

Now we can substitute the results back into the original expression:
\[
(3 - \sqrt{2}) + (5 + \sqrt{2}) = 3 - \sqrt{2} + 5 + \sqrt{2}
\]
The \(-\sqrt{2}\) and \(+\sqrt{2}\) cancel out:
\[
= 8
\]

Thus, the final result of the expression is:
\[
\boxed{8}
\]