Henry Ernest Dudeney/Modern Puzzles/21 - Their Ages

Modern Puzzles by Henry Ernest Dudeney: $21$

Their Ages

If you add the square of Tom's age to the age of Mary,

the sum is $62$;

but if you add the square of Mary's age to the age of Tom,

the result is $176$.

Can you say what are the ages of Tom and Mary?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Age and Kinship Puzzles: $21$. -- Their Ages
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Age Puzzles: $32$. Their Ages