Preliminary open-label studies have suggested that non-invasive brain stimulation methods of both transcranial direct current stimulation (tDCS) and repetitive transcranial magnetic stimulation (rTMS) have clinical benefits for improving psychological and eating disorder related symptoms, which can persist at long-term follow ups after acute treatment (i.e., at 6 and 12 months). Here the investigators propose to conduct the first double-blinded, randomised sham-controlled study to directly compare the therapeutic effectiveness and acceptability of both treatment modalities. Participants will be recruited and treated at one inpatient setting (Northside Clinic, St Leonards, Sydney). This facility is one of the largest specialist eating disorder settings in Australia with approximately 130 new admissions every year (2019 data). All participants who give consent and who fulfill the eligibility criteria will be randomised to receive active tDCS, sham (placebo) tDCS, active rTMS or sham rTMS over 8 weeks. Trial participants, their treating psychiatrist, ward staff, and a study staff member (who will conduct blinded assessments of mood secondary outcome measures) will be blinded after assignment to intervention until the database is locked and the primary analysis completed. All participants will complete assessments of eating disorder symptoms, mood, psychological symptoms, neurocognition and functioning at baseline, end of week 4, 8 and 20. Expected outcomes include data on the relative effectiveness and acceptability for both treatment modalities in the inpatient and at-home setting (i.e., for at-home tDCS). The investigators expect that both active treatment arms will produce clinical benefits and have high acceptability, and that clinical benefits will be maintained with long-term at-home tDCS continuation treatment. These outcomes have potential to assist in reducing hospital stay and emergency re-admissions and improving day to day functioning in participants. Health economic data for both treatment modalities will additionally have utility from a service perspective, given the disparity in resource requirements between the two treatments (TMS, tDCS) in terms of costs for patients and access to treatment for people living in remote and rural areas (i.e., for at-home tDCS).