The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is :

If Δl be the elongation due to tension T, then T ∝ Δl
Thus, T1 ∝ Δl1 and T2 ∝ Δl2 where l=natural length of wire.
So, T1/T2 = Δl1/Δl2 (1)
Now, l1 = l + Δl1 and l2 = l + Δl2
So, l1T2 = T2l + T2Δl1.. (2)
and l2T1 = T1l + T1Δl2.. (3)
using (1), (3) becomes l2T1 = T1l + T2Δl1.. (4)
(2) - (4) → l1T2 - l2T1 = T2l - T1l
or l = l1T2 - l2T1 / T2 - T1