Sum of all matrix entries

For large $n\times n$ symmetric matrices $T,$ where $n\approx10000,$ is there an efficient way of computing the total sum $S$ of its entries in Mathematica without having to loop over all its entries? i.e. $S=\sum_{i,j} t_{ij},$ for every $i,j.$ The fact that it's symmetric does help already as we only have to sum over one of its triangular parts.