To calculate \( C \) and \( D \), we will simplify each expression step by step.

### Calculation of \( C \)

We need to compute:

\[
C = \sqrt{49 - 12\sqrt{5}} - \sqrt{49 + 12\sqrt{5}}
\]

We can simplify each square root individually.

1. For \( \sqrt{49 - 12\sqrt{5}} \):
- Let \( 49 - 12\sqrt{5} = (\sqrt{a} - \sqrt{b})^2 \).
- Expanding: \( a + b - 2\sqrt{ab} = 49 - 12\sqrt{5} \).
- Thus, we have \( a + b = 49 \) and \( 2\sqrt{ab} = 12\sqrt{5} \), leading to \( \sqrt{ab} = 6\sqrt{5} \), hence \( ab = 180 \).

We solve the equations:
- \( x + y = 49 \)
- \( xy = 180 \)

This is the quadratic \( t^2 - 49t + 180 = 0 \). The roots will be:
\[
t = \frac{49 \pm \sqrt{49^2 - 4 \cdot 180}}{2}
\]

The discriminant calculation:
\[
49^2 - 720 = 2401 - 720 = 1681,
\]
and taking the square root gives \( \sqrt{1681} = 41 \).

Thus:
\[
t = \frac{49 \pm 41}{2} \Rightarrow t_1 = 45, \, t_2 = 4.
\]

Therefore:
- \( a = 45 \) and \( b = 4 \) (or vice versa).

We confirm:
\[
\sqrt{49 - 12\sqrt{5}} = \sqrt{45} - \sqrt{4} = 3\sqrt{5} - 2.
\]

2. For \( \sqrt{49 + 12\sqrt{5}} \):
- Similar approach:
- Let \( 49 + 12\sqrt{5} = (\sqrt{c} + \sqrt{d})^2 \).

Develop similar equations:
- \( c + d = 49 \)
- \( cd = 180 \).

This leads to the same quadratic and roots:
\[
t = 45, \, t = 4.
\]

Thus:
\[
\sqrt{49 + 12\sqrt{5}} = \sqrt{45} + \sqrt{4} = 3\sqrt{5} + 2.
\]

Now, substitute back into \( C \):
\[
C = (3\sqrt{5} - 2) - (3\sqrt{5} + 2) = -4.
\]

### Calculation of \( D \)

Next, we compute:

\[
D = \sqrt{29 + 12\sqrt{5}} - \sqrt{29 - 12\sqrt{5}}.
\]

Following a similar procedure:

1. For \( \sqrt{29 + 12\sqrt{5}} \):
- \( 29 + 12\sqrt{5} = (\sqrt{a} + \sqrt{b})^2 \).
- This gives \( a + b = 29 \) and \( ab = 180 \).

Solving \( t^2 - 29t + 180 = 0 \):
\[
29^2 - 720 = 841 - 720 = 121.
\]
Thus:
\[
t = \frac{29 \pm 11}{2} \Rightarrow t_1 = 20, \, t_2 = 9.
\]
So \( \sqrt{29 + 12\sqrt{5}} = \sqrt{20} + \sqrt{9} = 2\sqrt{5} + 3 \).

2. For \( \sqrt{29 - 12\sqrt{5}} \):
- Similar procedure leads to the same quadratic, giving:
\[
\sqrt{29 - 12\sqrt{5}} = \sqrt{20} - \sqrt{9} = 2\sqrt{5} - 3.
\]

Now, substitute back into \( D \):
\[
D = (2\sqrt{5} + 3) - (2\sqrt{5} - 3) = 6.
\]

### Final Answers

Thus, the results are:
\[
C = -4, \quad D = 6.
\]