Let's solve the given expressions step by step.

1) \( B = 2\sqrt{2} + \sqrt{(\sqrt{8} - 3)^2} \)

First, simplify the term inside the square root:
\[ \sqrt{8} = 2\sqrt{2} \]

So,
\[ (\sqrt{8} - 3)^2 = (2\sqrt{2} - 3)^2 \]

Since \((a - b)^2 = a^2 - 2ab + b^2\), we get:
\[ (2\sqrt{2} - 3)^2 = (2\sqrt{2})^2 - 2 \cdot 2\sqrt{2} \cdot 3 + 3^2 \]
\[ = 8 - 12\sqrt{2} + 9 \]
\[ = 17 - 12\sqrt{2} \]

Now, take the square root:
\[ \sqrt{(2\sqrt{2} - 3)^2} = |2\sqrt{2} - 3| \]

Since \(2\sqrt{2} \approx 2.828\) and \(2\sqrt{2} - 3 \approx -0.172\), the absolute value is:
\[ |2\sqrt{2} - 3| = 3 - 2\sqrt{2} \]

So,
\[ B = 2\sqrt{2} + (3 - 2\sqrt{2}) \]
\[ B = 3 \]

2) \( B = \sqrt{(\sqrt{7} - 4)^2} + \sqrt{7} \)

First, simplify the term inside the square root:
\[ (\sqrt{7} - 4)^2 = (\sqrt{7})^2 - 2 \cdot \sqrt{7} \cdot 4 + 4^2 \]
\[ = 7 - 8\sqrt{7} + 16 \]
\[ = 23 - 8\sqrt{7} \]

Now, take the square root:
\[ \sqrt{(\sqrt{7} - 4)^2} = |\sqrt{7} - 4| \]

Since \(\sqrt{7} \approx 2.646\) and \(\sqrt{7} - 4 \approx -1.354\), the absolute value is:
\[ |\sqrt{7} - 4| = 4 - \sqrt{7} \]

So,
\[ B = (4 - \sqrt{7}) + \sqrt{7} \]
\[ B = 4 \]

Therefore, the simplified results are:
1) \( B = 3 \)
2) \( B = 4 \)