A positive integer is called [i]sabroso [/i]if when it is added to the number obtained when its digits are interchanged from one side of its written form to the other, the result is a perfect square. For example, $143$ is sabroso, since $143 + 341 =484 = 22^2$. Find all two-digit sabroso numbers.
1. Let the two-digit number be represented as $\overline{ab}$, where $a$ and $b$ are the digits. This number can be written as $10a + b$.
2. When the digits are interchanged, the number becomes $\overline{ba}$, which can be written as $10b + a$.
3. According to the problem, the number is sabroso if the sum of the number and its digit-reversed form is a perfect square. Therefore, we need:
   \[
   (10a + b) + (10b + a) = 11a + 11b = 11(a + b)
   \]
4. For $11(a + b)$ to be a perfect square, $a + b$ must be such that $11(a + b)$ is a perfect square. Let $11(a + b) = k^2$ for some integer $k$.
5. Since $a$ and $b$ are digits of a two-digit number, $a$ ranges from 1 to 9 and $b$ ranges from 0 to 9. Therefore, $a + b$ ranges from 1 to 18.
6. We need to find $a + b$ such that $11(a + b)$ is a perfect square. The possible values of $k^2$ that are multiples of 11 and within the range of $11 \times 1$ to $11 \times 18$ are:
   \[
   11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198
   \]
7. Among these, the only perfect square is $121$, which corresponds to $k = 11$. Therefore:
   \[
   11(a + b) = 121 \implies a + b = 11
   \]
8. Now, we find all pairs $(a, b)$ such that $a + b = 11$ and $a$ and $b$ are digits:
   \[
   (a, b) = (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2)
   \]
9. The corresponding two-digit numbers are:
   \[
   29, 38, 47, 56, 65, 74, 83, 92
   \]
10. Verify that each of these numbers is sabroso:
    - $29 + 92 = 121 = 11^2$
    - $38 + 83 = 121 = 11^2$
    - $47 + 74 = 121 = 11^2$
    - $56 + 65 = 121 = 11^2$
    - $65 + 56 = 121 = 11^2$
    - $74 + 47 = 121 = 11^2$
    - $83 + 38 = 121 = 11^2$
    - $92 + 29 = 121 = 11^2$

All these numbers satisfy the condition of being sabroso.

The final answer is $\boxed{29, 38, 47, 56, 65, 74, 83, 92}$