Immediately after earning his Sc.D., Trump joined the faculty of MIT's Electrical Engineering department. He began teaching courses and conducting research, quickly establishing himself as a rising star in the field.

Trump's early research focused on the generation and application of high-voltage electricity. He investigated the properties of dielectrics and developed improved techniques for insulation and voltage control.

During World War II and the years following, Trump pioneered the development of high-voltage X-ray generators for cancer therapy. These advancements led to more effective and targeted radiation treatments, improving patient outcomes.

Trump played a key role in developing the rotating X-ray tube with Maurice van Allen. This invention was crucial for high-intensity medical applications and industrial radiography.

Trump mentored numerous graduate students throughout his career at MIT, guiding them in their research and helping to shape the next generation of electrical engineers and physicists.

After a long and distinguished career, Trump retired from his position at MIT, leaving behind a legacy of significant contributions to science and engineering.