To gleam is to reflect a bright light, usually in a positive or beautiful way. When your eyes are gleaming, it means you are happy or excited.
Ex: We polished the silver and now it just gleams. It reflects all the light of the sun in the daytime and looks gorgeous.
Ex: When mom came home she looked at the floors that we had washed and was pleasantly surprised. They were so clean and shiny that they gleamed.
Something that is planned or just being thought about but not yet started is just a gleam in one's eye.
Ex: Ellie's English school is one of the most successful businesses in town these days, but I remember when it was just a gleam in her eye. It really hasn't been that long since she started putting it together.
Ex: Jake has some interesting ideas for his final project, but they're really still just a gleam in his eye. He'd better get started soon or he won't have enough time to finish.
To beam is to shine or give off bright light, usually in a linear way like from the sun or the headlights of a car. This kind of line of light is also called a beam.
Ex: The sky was so beautiful today. There were some clouds, but the sunlight just beamed through with long lines straight from heaven.
Ex: When Sharon came out of the house to see who had arrived, she could see almost nothing because of the glare from the headlight's bright beams.
The extra bright lights on a car are also called high beams. Someone who is very happy and excited about something is beaming (with excitement).
Ex: Terry told Gemma to turn on the high beams if she couldn't see. They shine on a wider part of the road and make it easier.
Ex: When Alison found out that she got the new job in Spain, she was just beaming with excitement. I haven't seen her this happy in years.