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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The teenagers Sam and Jo notice the following facts about their ages: The difference between the squares of their ages is four times the sum of their ages. The sum of their ages is eight times the difference between their ages. What is the age of the older of the two?

(A) $15$ (B) $16$ (C) $17$ (D) $18$ (E) $19$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.