This paper presents two different low-complexity methods for obtaining the secrecy capacity of multiple-input multiple-output (MIMO) wiretap channel subject to a sum power constraint (SPC). The challenges in deriving computationally efficient solutions to the secrecy capacity problem are due to the fact that the secrecy rate is a difference of convex functions (DC) of the transmit covariance matrix, for which its convexity is only known for \emph{the degraded case}. In the first method, we capitalize on the accelerated DC algorithm, which requires solving a sequence of convex subproblems. In particular, we show that each subproblem indeed admits a water-filling solution. In the second method, based on the equivalent convex-concave reformulation of the secrecy capacity problem, we develop a so-called partial best response algorithm (PBRA). Each iteration of the PBRA is also done in closed form. Simulation results are provided to demonstrate the superior performance of the proposed methods.