Not as bad as you might think.....
CE = 2sqrt 61 = sqrt 244
AD = sqrt 601
Note that we have this system
AD^2 = (BC/2)^2 + (AB)^2
CE^2 = (BC)^2 + (AB/2)^2 simplify
601 = BC^2/4 + AB^2
244 = BC^2 + (AB/2)^2
601 = BC^2 /4 + AB^2
244 = BC^2 + AB^2/4 mutiply the top equation through by -4
-2404 = -BC^2- 4AB^2
244 = BC^2 + AB^2/4 add these
-2160 = -(15/4)AB^2
(-2160) * (-4/15) =AB^2 = 576
AB = sqrt (576) = 24
To find BC
244 = BC^2 + (24/2)^2
244 = BC^2 + 144
100 = BC^2
10= BC
Hypotenuse = sqrt [ 24^2 + 10^2 ] = sqrt [676 ] = 26