T. Ernest Robertson appears to have studied at Glasgow and at Trinity College, Dublin. He arrived in Johannesburg in February 1904 to take up his appointment as acting professor of mining and metallurgy at the newly established Transvaal Technical Institute. Classes started in March that year. In 1906 the Institute became the Transvaal University College (Johannesburg branch) and by 1909 Robertson was its lecturer in surveying. In 1910 the Johannesburg branch of the College became the South African School of Mines and Technology (later the University of the Witwatersrand) and that same year Robertson became Dean of the student residence, College House. In 1911 he was promoted to professor of surveying, a post he held until 1913.
Robertson was a Fellow of the (British) Geological Society. He became a member of the Chemical, Metallurgical and Mining Society of South Africa in 1904 and of the British Association for the Advancement of Science in 1905. By 1906 he was also a member of the South African Association for the Advancement of Science. That year he published a paper in the Journal of the Institute of Land Surveyors of the Transvaal (Vol. 1(4), pp. 123-132) on "The relation between the magnitude of errors of observation and their mode of occurrence", in which he compared the observed distribution of errors in angular measurements to the Gaussian distribution, both before and after the rejection of extreme values.