Solve Delay and Sum Algorithm

Question

By using the formulas $$ \begin{split} r_{ij}(t)&=\sqrt{u_{ij}(t)^2}\\ t_{ij}(x,y)& = t_\mathrm{on}+\frac{\sqrt{(x_i-x)^2+(y_i-y)^2}+\sqrt{(x_j-x)^2+(y_j-y)^2}}{c_\mathrm{g}}\\ E(x,y) &=\frac{1}{N_\mathrm{p}}\sum_{i=1}^{N-1} \sum_{j=i+1}^{N} r_{ij}\big(t_{ij}(x,y)\big) \end{split} $$ I want to generate an image through Delay and Sum algorithm. I have calculated $r_{ij}(t)$ which is nothing but a $n$-tuple of signals in the time domain ($1\times n$ matrices), and the $t_{ij}(x,y)$ ($n\times n$ matrices) which is the required by the signals to reach the point $(x,y)$. $(x_i,y_i)$ and $(x_j,y_j)$ are fixed values.
In sum, I have calculate both the needed terms, but I can't figure out how to determine $E(x,y)$ and calculate $r_{ij}\big(t_{ij}(x,y)\big)$ term in mathlab or python. Could please someone guide me explain how to determine $E(X,y)$? Thank you