I will assume you are talking about the open wound at the base of the trunk as being the "fungus"? If not, please let me know.
This wound appears to have been there for some time. The exposed wood is likely decaying (a natural occurrence and fungi play a role). Trees never "heal" a wound; instead they compartmentalize wounds by sending defense chemicals to the site. If it works, the wound and any decay is "compartmentalized" from the rest of the tree to prevent spread throughout the tree; as long as the tree remains healthy. There is nothing you can do for the wound, but keep the tree healthy with correct watering and preventing additional wounds. Since the tree is in a lawn, and I assume the lawn is fertilized; do not add additional fertilizer just for the tree as too much nitrogen can further stress the tree. Do not cover the wound with any kind of wound dressing or trunk wrap. This holds moisture in the wound and can increase decay.
Since this is in a backyard, and children play on and near the tree; it bears close watching for safety. The tree can live for many years. Here is what to watch for:
1. Signs of increased decay that may be spreading (you can gently tap on the trunk above the wound and to the sides and opposite side with the flat side of a hammer to see if the trunk sounds hollow, for example. A sign decay is spreading.
2. Watch the crown of the tree for signs of twig/branch die back and thinning. Again, a sign there may be more going on within the trunk than is visible on the outside.
3. Watch the wound for signs of insect activity. The wound could be treated with an insecticide if needed.
3. It would be wise to have a certified Arborist check the tree as well.
Please let me know if you have additional questions.