Time-domain single-channel speech enhancement (SE) still remains challenging to extract the target speaker without any prior information on multi-talker conditions. It has been shown via auditory attention decoding that the brain activity of the listener contains the auditory information of the attended speaker. In this paper, we thus propose a novel time-domain brain-assisted SE network (BASEN) incorporating electroencephalography (EEG) signals recorded from the listener for extracting the target speaker from monaural speech mixtures. The proposed BASEN is based on the fully-convolutional time-domain audio separation network. In order to fully leverage the complementary information contained in the EEG signals, we further propose a convolutional multi-layer cross attention module to fuse the dual-branch features. Experimental results on a public dataset show that the proposed model outperforms the state-of-the-art method in several evaluation metrics. The reproducible code is available at https://github.com/jzhangU/Basen.git.