In this paper, we analyze (for the first time in literature) the secrecy performance of a two-hop cooperative network in which all the nodes are of the energy-harvesting self-sustaining type. Both source and relay harvest energy from a power beacon (PB) and employ the harvest-use (HU) architecture. We consider optimal combining of the direct and relayed signals at the destination and eavesdropper. We do not assume any channel state information (CSI) at the source. We derive an approximate closed-form expression for secrecy outage probability assuming selective decode-and-forward (SDF) protocol at the relay. We demonstrate that secrecy outage is a convex function of the transmit power of PB. Further, the security-reliability trade-off (SRT) is analyzed to highlight the trade-off between outage and intercept probability. Computer simulations validate the derived analytical expressions