Two Differences to a Sum

Two positive numbers are such that their difference is 7 and the difference of their squares is 105. What is their sum?
Your task:

1. Show your kid brother (or sister) what this means by solving it in an arithmetical manner. Be patient.
2. Show your parents how much you’ve learned in Algebra 1 this year by solving it with basic algebra. This means, you just demonstrate what the sum is, without determining what the two numbers are.
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