Understanding the Problem
To solve for two numbers given their ratio and difference, we can use algebraic methods.

Step 1: Define the Variables
Let the two numbers be represented as:
- Number 1 = 7x
- Number 2 = 10x
Here, 'x' is a common multiplier.

Step 2: Set Up the Equation
According to the problem, the difference between the two numbers is given as:
- Difference = Number 2 - Number 1
- Difference = 10x - 7x = 3x
We know the difference is 105, so we can set up the equation:
- 3x = 105

Step 3: Solve for x
To find the value of x, divide both sides of the equation by 3:
- x = 105 / 3
- x = 35

Step 4: Calculate the Numbers
Now, substitute the value of x back into the expressions for the numbers:
- Number 1 = 7x = 7 * 35 = 245
- Number 2 = 10x = 10 * 35 = 350

Final Result
Thus, the two numbers are:
- Number 1: 245
- Number 2: 350

Conclusion
The two numbers with a ratio of 7:10 and a difference of 105 are 245 and 350. This method of setting up equations based on the given conditions is a powerful technique in solving ratio and difference problems.