Question 198390
Let  x  = 1st  integer,   and,,,x+1 =  2nd  integer
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sum  of  squares  is ,  x^2 + (x+1)^2 = x^2 + x^2 +2x +1 = 2x^2 +2x +1  = 365
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simplifying,  2x^2 +2x -364 =0,  or  x^2 +x - 182 =0
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factoring,,(x+14) (x-13) =0
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x+14  =0,,, or  x=  -14  with  next  integer  -13
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or  x-13 = 0,  with  x=13,  and  next  integer  14
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both  sets  check
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