What is the process by which glucose can pass through a cell membrane by combining with special carrier molecules?

The process you are referring to is facilitated diffusion.
No additional energy is required to transport glucose across a cell membrane. However,
there must be a concentration gradient(difference) outside and inside the cell for
transport to occur. If both sides of the membrane are equal, no net movementof glucose
molecules will occur. If glucose is outside the membrane in a high concentration
relative to inside the membrane, it will bind to a specific carrier molecule in the
membrane. A change occurs in the membrane exposing the glucose to the inside of the
cell. Once inside, it changes to glucose-6 phosphate. Because of this,  the level of
glucose inside the cell is close to zero. This maintains the concentration gradient
being higher outside the cell compared to inside the cell. This insures that glucose
will move into the cell from high concentration to low.