Temperature and pressure are inversely related, so how, in the core of the Earth, are both temperature and pressure high?

Temperature and pressure are not inversely proportional. In fact, if the volume is held constant, temperature and pressure are directly proportional to each other. One way to think about it is to understand what happens when we increase the temperature of a substance. When the temperature increases, the molecules comprising the substance gain kinetic energy and start moving faster. When that happens, their collisions with each other and with the material they are held in (especially for fluids) increases and this causes an increase in temperature. The same is observed when we cook something in a pressure cooker or boil water for making tea or coffee.

Thus, it is entirely feasible for the temperature and pressure to increase simultaneously, provided the volume is held constant. In the earth's core, the temperature and pressure both are very high, and it is estimated that the core is divided into two parts. The external layer is liquid, while the inner core is solid (due to very high pressures, iron cannot melt, even at high enough temperatures).

Hope this helps.