The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. Find both the numbers.

Let the tens digit be $x$ and units digit be $y$.

Original number = $10x + y$;

Reversed number = $10y + x$.

According to problem,

$$(10x + y) + (10y + x) = 143$$

$$\Rightarrow 11x + 11y = 11(x + y) = 143$$

$$\Rightarrow x + y = 13.$$

Also $|x - y| = 3$.

Case 1: $x - y = 3$ and $x + y = 13$

$$\Rightarrow x = 8, y = 5 \Rightarrow \text{Number} = 85$$

Case 2: $y - x = 3$ and $x + y = 13$

$$\Rightarrow y = 8, x = 5 \Rightarrow \text{Number} = 58$$

Hence, the two numbers are 58 and 85.