The three-page message urges voters to consider their Christian heritage and "obligations to future generations".
It also calls on politicians to "renew and re-imagine" the UK's shared values amid divisions of recent years.
There needs to be "serious solutions" to home-building and a "flourishing" health service, the letter says.
In the pastoral letter to parishes and chaplaincies, the Church of England's most senior clergymen -the Most Reverend Justin Welby, the Archbishop of Canterbury, and the Most Reverend John Sentamu, the Archbishop of York - allude to the UK's negotiations with the EU over Brexit.
The letter says the election "is being contested against the backdrop of deep and profound questions of identity.
"Opportunities to renew and re-imagine our shared values as a country and a United Kingdom of Great Britain and Northern Ireland only come around every few generations...
"If our shared British values are to carry the weight of where we now stand and the challenges ahead of us, they must have at their core, cohesion, courage and stability."
The letter refers to the benefits of "education for all, the need for urgent and serious solutions to our housing challenges, the importance of creating communities as well as buildings, and a confident and flourishing health service that gives support to all - especially the vulnerable - not least at the beginning and end of life".
The archbishops go on to call for a "just economy" - one not over-reliant on debt that "risks crushing those who take on too much".
They add: "Courage also demands a radical approach to education, so that the historic failures of technical training and the over-emphasis on purely academic subjects are rebalanced."
The Church leaders also say that refugees and migrants should be given a "generous and hospitable" welcome but politicians should not be "deaf to the legitimate concerns" of communities.
And they say the religious faith of election candidates "should not be treated by opponents as a vulnerability to be exploited".
A letter to parishioners published in the run-up to the 2015 general electionattracted criticism and claims of pro-Labour bias after it called for a review of the UK's nuclear weapons.
The Archbishops of Canterbury and York have raised concerns about housing, the NHS and poverty in a general election letter to Anglican churchgoers.