2. Ivana chose two numbers $a$ and $b$ from the set $\{1,2,3,4, \ldots, 25,26\}$. The product $a \cdot b$ is equal to the sum of the remaining 24 numbers in that set of numbers. What is the value of the expression $|a-b|$?
First method:

Assume $a \geq b$.

Since $a$ and $b$ are from the set $\{1,2,3,4, \ldots, 25,26\}$ and their product is equal to the sum of the remaining 24 numbers, we have $a+b+a \cdot b=1+2+3+4+\ldots+25+26$ or $a+b+a \cdot b=351$.

Adding 1 to both sides of the equation, we get $a+b+a \cdot b+1=352$.

By factoring the left side, we obtain $(1+b) \cdot(1+a)=352$.

This means that the number 352 is the product of two natural numbers $a+1$ and $b+1$.

By factoring the number 352 into prime factors, we get $352=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 11$.

Since the numbers $a$ and $b$ are from the set $\{1,2,3,4, \ldots, 25,26\}, a \geq b$, it follows that $a+1=22$ and $b+1=16$.

Thus, $a=21$ and $b=15$.

Therefore, $|a-b|=6$.