To find the difference between two numbers, we need to first find the two numbers.

Given:
LCM (Least Common Multiple) = 2376
HCF (Highest Common Factor) = 22
Sum of the numbers = 682

Step 1: Finding the Two Numbers
We know that the product of two numbers is equal to the product of their LCM and HCF. Let's denote the two numbers as 'a' and 'b'.

LCM * HCF = a * b
2376 * 22 = a * b
52272 = a * b

Step 2: Finding the Two Numbers Using the Sum of Numbers
We also know that the sum of two numbers is equal to the sum of their LCM and HCF multiples. Let's use this information to find the two numbers.

a + b = LCM + HCF
a + b = 2376 + 22
a + b = 2398

We now have two equations:
a * b = 52272
a + b = 2398

Step 3: Solving the Equations
We can solve these equations simultaneously to find the two numbers. Let's solve them using substitution.

Rearrange the second equation to solve for 'b':
b = 2398 - a

Substitute this value of 'b' into the first equation:
a * (2398 - a) = 52272
2398a - a^2 = 52272
a^2 - 2398a + 52272 = 0

Using the quadratic formula, we can solve for 'a':
a = (2398 ± √(2398^2 - 4 * 1 * 52272)) / 2
a = (2398 ± √(5750404 - 209088)) / 2
a = (2398 ± √5541316) / 2
a = (2398 ± 2356) / 2

We get two possible values for 'a':
a1 = (2398 + 2356) / 2 = 4754 / 2 = 2377
a2 = (2398 - 2356) / 2 = 42 / 2 = 21

Step 4: Finding the Other Number
Now that we have the value of 'a', we can find the corresponding value of 'b'.

Using the equation a + b = 2398, we substitute the value of 'a' to find 'b':
2377 + b = 2398
b = 2398 - 2377
b = 21

So, the two numbers are 2377 and 21.

Step 5: Finding the Difference
To find the difference between the two numbers:
Difference = Larger Number - Smaller Number
Difference = 2377 - 21
Difference = 2356

Therefore, the difference between the two numbers is 2356.