A closed loop traverse has been established that contains five TBMs $($A$-$E$).$ The stations have been labelled in a clockwise rotation; hence the external included angles were measured when establishing the traverse, and TBM A has the coordinates $75m,75m($easting and northing respectively$).$ The theoretical angle check indicated a $20"$ misclosure and the use of the Bowditch method indicates a linear misclosure of $1$ in $13,917.$ Both of which were deemed acceptable. The Bowditch correction applies a change in easting and northing $(E$ and $N,$ respectively$)$ to the change in easting and northing calculated $(\frac{?}{{?}_{\frac{?}{?}}E}$ and $\frac{?}{{?}_{\frac{?}{?}}N},$ respectively$)$ when manipulating the whole circle angles and horizontal distances to determine the coordinates for each TBM within the traverse to produce corrected changes $(E_{\text{c}\text{o}\text{r}\text{r}\text{e}\text{c}\text{t}\text{e}\text{d}}$ and $N_{\text{c}\text{o}\text{r}\text{r}\text{e}\text{c}\text{t}\text{e}\text{d}},$ respectively$)$ such that: $N_{\text{c}\text{o}\text{r}\text{r}\text{e}\text{c}\text{t}\text{e}\text{d}}=N+-N$

$\backslash$table$[[$Station$,$line,$\backslash$table$[[$Horizontal$],[$distance $($m$)]],\backslash$Delta E$($m$),\backslash$Delta N$($m$),$E$,$N$],[$A$,-,-,-,-,75\mathrm{.}000,75\mathrm{.}000],[$B$,$A$-$B$,33\mathrm{.}333,0\mathrm{.}000,33\mathrm{.}333,75\mathrm{.}000,108\mathrm{.}333],[$C$,$B$-$C$,66\mathrm{.}423,64\mathrm{.}162,17\mathrm{.}184,139\mathrm{.}162,125\mathrm{.}517],[$D$,$C$-$D$,19\mathrm{.}067,10\mathrm{.}351,-16\mathrm{.}012,149\mathrm{.}513,109\mathrm{.}505],[$E$,$D$\_$E$,50\mathrm{.}035,-47\mathrm{.}892,-14\mathrm{.}485,101\mathrm{.}621,95\mathrm{.}020],[$A$,$E$-$A$,33\mathrm{.}314,-26\mathrm{.}633,-20\mathrm{.}012,74\mathrm{.}988,75\mathrm{.}008]]$

The calculation for the coordinates in the traverse was started but not completed. Calculate the easting coordinate value for TBM E by applying the Bowditch correction. Please state the value $($in metres$)$ to three decimal places